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Autor Díaz Díaz, Jesús Ildefonso |
Documentos disponibles escritos por este autor (214)
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Díaz Díaz, Jesús Ildefonso ; Tello, Lourdes | Department of Mathematics Texas State University | 2007We study a three dimensional climate model which represents the coupling of the mean surface temperature with the ocean temperature. We prove the existence of a bounded weak solution by a fixed point argument.![]()
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We start by studying the finite extinction time for solutions of the abstract Cauchy problem u(t) + Au + Bu = 0 where A is a maximal monotone operator and B is a positive operator on a Hilbert space H. We use a suitable spectral energy method to[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Faghloumi, Ch. | Real Academia Ciencias Exactas Físicas Y Naturales | 2008An application of the results of this paper proves that there is not always an economic benefit when destroying the environment for planting an alternative industrial project. Our criterion, to act, to delay or to deny the industrial investment [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Bejenaru, Ioan ; Vrabie, Ioan I. | Texas State University, Department of Mathematics | 2001The authors obtain an approximate controllability result for the nonlinear equation $y'+Ay+F(t,y)y=h(t)$ with the initial condition where $x$ is the control and $A$ generates a $C_0$-semigroup in a Hilbert space. The Schauder fixed poi[...]![]()
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The purpose of this paper is to study the problem (P) ??u+u??=f in ?, u=0 on ??, u???L1(?), u> 0 in ?, where ? is a bounded smooth open set of RN, f?0, f?L1(?) and 0![]()
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Díaz Díaz, Jesús Ildefonso ; Lerena Guil, María Belen ; Padial Molina, Juan Francisco ; Rakotoson, Jean Michel Theresien | Elsevier | 2004-04-10We prove the existence and the regularity of weak solutions of a nonlocal elliptic–parabolic free-boundary problem involving the notions of relative rearrangement and monotone rearrangement. The problem arises in the study of the dynamics of a m[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Hetzer, G. ; Tello del Castillo, Lourdes | Pergamon-Elsevier Science | 2006-05-01Energy balance climate models of Budyko type lead to reaction-diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line). Here we introduce a Babuska-Duhem hysteresis in[...]![]()
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We give a simple mathematical proof of the popular strategy "donít put o§ for tomorrow what you can do today" by using the HUM method due to Jacques-Louis Lions for the controllability of linear systems.![]()
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We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.[...]![]()
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Wt,give some negative and positive results on the approximate controllability of the Stokes system formulated on a cylinder Omega = G x R of R-3 when the control is a density of external unidirectional forces. We distinguish the case where the d[...]![]()
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This paper concerns the blow-up behavior of large radial solutions of polyharmonic equations with power nonlinearities and positive radial weights. Specifically, we consider radially symmetric solutions of mu = c(|x|)|u| p on an annulus {x ? Rn [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Hetzer, Georg | Department of Mathematics Texas State University | 2007This note is devoted to stick-slip aspects of the motion of a dry friction damped oscillator under weak irregular forcing. Our main result complements[10, Theorem 3.(a)] and is also related to [1], where a non-Lipschitz model for Coulomb frictio[...]![]()
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Given a bounded open set Omega subset of R-n and a continuous convex function Phi: L-2(Omega) -> R, let us consider the following damped wave equation u(tt) - Delta u + partial derivative Phi(u(t)) 0, (t, x) is an element of (0, +infinity) x Om[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Casal, Alfonso C. ; Vegas Montaner, José Manuel | Dynamic Publishers, Inc. | 2009Blow-up phenomena are analyzed for both the delay-differential equation (DDE) u'(t) = B'(t)u(t - tau), and the associated parabolic PDE (PDDE) partial derivative(t)u=Delta u+B'(t)u(t-tau,x), where B : [0, tau] -> R is a positive L(1) function w[...]![]()
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The authors study the behaviour of the solution of the Signorini problem at the boundary. In particular a necessary and quasi-sufficient condition for the existence of a nonempty coincidence set and some estimates on the location of the coincide[...]![]()
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We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear problems of eigenvalue type with possibly sin[...]![]()
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The author studies by the local energy method the compactness of the support of the solutions to nonlinear elliptic or parabolic equations (in this last case also the Stefan-like case is considered).![]()
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We show some compactness properties of the operator f--u, where u is the solution of the nonlinear diffusion equation ut???(u)=f on (0,T)×? associated with the parabolic boundary conditions ?(u)=0 on (0,T)×?? and u(0,?)=u0(?) on ?, u0 a given fu[...]![]()
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The authors study the nonlinear porous media type equation ut(t,x)???(u(t,x))=0 for (t,x)?(0,?)×?, ?(u(t,x))=0 for (t,x)?(0,?)×??, u(0,x)=u0(x) for x??, with ? an open set in Rn, and ? a regular, real, continuous, nondecreasing function. In the [...]![]()
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The (simplified) Backus' Problem (BP) consists in finding a harmonic function u on the domain exterior to the three dimensional unit sphere S, such that u tends to zero at infinity and the norm of the gradient of u takes prescribed values g on S[...]![]()
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Global time-delay autosynchronization is known to control spatiotemporal turbulence in oscillatory reactiondiffusion systems. Here, we investigate the complex Ginzburg-Landau equation in the regime of spatiotemporal turbulence and study numerica[...]![]()
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We consider the Cauchy problem ut = ?(u)xx + ?(u), (t, x) ? R+ × R, u(0, x) = u0(x), x ? R, when the increasing function ? satisfies that ?(0) = 0 and the equation may degenerate at u = 0 (in the case of ?? (0) = 0). We consider the case of u0 ?[...]![]()
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Bui, L.T.T. ; Dao, A. N ; Díaz Díaz, Jesús Ildefonso | Texas State University, Department of Mathematics | 2017We prove the existence of solutions of the viscous Cahn-Hilliard equation in whole domain when the nonlinear term in the second order diffusion grows as uq for the critical case when N > = 3. Our results improve the ones in [9, 12].![]()
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In the book by U. Hornung, Chapter 6, the author proposes an homogenization strategy for the effective behavior of some chemical processes involving adsorption and reactions arising in porous media. Rigorous proofs of the convergence results are[...]![]()
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This paper gives a very brief review of some properties of solutions of quasilinear scalar elliptic and parabolic partial differential equations in a spatial domain ?. Emphasis is laid on nonlinearities which allow the support of the solutions t[...]![]()
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We present a new proof of comparison results via Steiner symmetrization for solutions of elliptic equations. This proof relies upon a "level sets" argument.![]()
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Díaz Díaz, Jesús Ildefonso ; Alvino, A. ; Trombetti, G. ; Lions, P.L. | John Wiley & SONS INC | 1996-03We give some comparison results for elliptic equations by using Steiner symmetrization.![]()
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Díaz Díaz, Jesús Ildefonso ; Rakotoson, Jean-Michel | Department of Mathematics Texas State University | 2014We revisit the regularity of very weak solution to second-order elliptic equations Lu = f in ? with u = 0 on ?? for f ? L1 (?, ?), ?(x) the distance to the boundary ??. While doing this, we extend our previous results(and many others in the lite[...]![]()
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In this paper we use some energy methods to study the location (and formation) of a free boundary arising in some unilateral problems, for instance, in the obstacle problem and the Stefan problem.![]()
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We obtain existence and uniqueness of solutions with compact support for some nonlinear elliptic and parabolic problems including the equations of one-dimensional motion of a non-newtonian fluid. Precise estimates for the support of these soluti[...]![]()
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Obtains existence and uniqueness of solutions with compact support for some nonlinear elliptic and parabolic problems including the equations of one-dimensional motion of a non-newtonian fluid. Precise estimates for the support of these solution[...]![]()
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In 1757, Leonhard Euler started the study of the tallest column, i.e. the shape of a stable column with the symmetry of revolution, such that it attains the maximum height once the total mass is prescribed, buckling due to the effect of a load s[...]![]()
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The authors study the nonlinear elliptic equation (*) ?div(a(x,u,Du))?div(?(u))+g(x,u)=f(x)in ? with the boundary condition (??) u=0 on ??, where ? is a bounded open subset of RN, A(u)=?div(a(x,u,Du)) is a nonlinear operator of Leray-Lions type[...]![]()
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The authors show the uniqueness and give some necessary and sufficient conditions for the existence of positive solutions of the equation ??pu=f(x,u), where ?p denotes the p-Laplacian and f(x,r)/rp?1 is assumed to be decreasing![]()
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The authors study the existence of weak solutions for the following system: ut???(u)?F(u,v), vt???(v)?G(u,v) in (0,T)×?, ?(u)=?(v)=0 on (0,T)×??, u(0,x)=u0(x), v(0,x)=v0(x) in the region ???Rn with smooth boundary ??. The functions ?,?:R?R are a[...]![]()
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We prove some existence (and sometimes also uniqueness) of weak solutions to some stationary equations associated to the complex Schrödinger operator under the presence of a singular nonlinear term. Among other new facts, with respect some previ[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Muñoz Montalvo, Ana Isabel ; Schiavi, Emanuele | Pergamon-Elsevier Science Ltd. | 2007-02This paper deals with the mathematical analysis of a nonlinear system of three differential equations of mixed type. It describes the generation of fast ice streams in ice sheets flowing along soft and deformable beds. The system involves a nonl[...]![]()
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The authors consider first-order equations in "conservation laws'' form perturbed by a semilinear nonlinearity of monotone type. The known existence and uniqueness results for conservation laws—results due to Kruzhkov—are easily adapted to this [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Bermejo, R. ; Carpio, Jaime ; Galán del Sastre, Pedro | Birkhäuser | 2008-07-11We present a finite element algorithm of a climate diagnostic model that takes as a climate indicator the atmospheric sea-level temperature. This model belongs to the category of energy balance models introduced independently by the climatologis[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Casal, A.C. ; Vegas Montaner, José Manuel | Pergamon-Elsevier Science | 2009-12-15We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type partial derivative u/partial derivative t - Lambda u = -M(t)u(t - tau, x) (1) with a delay term tau > 0, [...]![]()
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Casal, Alfonso C. ; Díaz Díaz, Jesús Ildefonso ; Vegas Montaner, José María | American Institute of Mathematical Sciences | 2011We prove that the mere presence of a delayed term is able to connect the initial state u0 on a manifold without boundary (here assumed given as the set ?? where ? is an open bounded set in RN ) with the zero state on it and in a finite time even[...]![]()
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The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions as[...]![]()
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The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions as[...]![]()
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We give conditions on the behaviour of the trace datum near the boundary of its support in order to know whether the free boundary given by the boundary of the support of the solution of suitable elliptic or parabolic semilinear problem is conne[...]![]()
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A mathematical model of general gas emitting systems is derived, and a sample of relevant mathematical results is offered. The present paper indicates that shallow subsurface gas sources in typical volcanic areas can be located if appropriate ph[...]![]()
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Arjona, Alicia ; Díaz Díaz, Jesús Ildefonso ; Fernández, J. | Universidad de Castilla-La Mancha | 2009Many volcanic constructs have geometric different shapes depending on different phenomena as parasitic cones, erosion or coral growth. In Lacey, Ockendon and Turcotte [11] the authors proposed a nonlinear model proving that the shape of volcanoe[...]![]()
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Shape ofmany volcanic edifices depend on different phenomena, such as parasitic cones, erosion or coral growth. A nonlinear model proposed in 1981 proves that the shape of volcanoes is determined by the hydraulic resistance to the flow of magma,[...]![]()
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In this Note, we study the existence and multiplicity of solutions, strictly positive or nonnegative having a dead core (where the solution vanishes) of a one-dimensional equation of eigenvalue type associated to a quasilinear operator with stro[...]![]()
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Coron, Jean-Michel ; Díaz Díaz, Jesús Ildefonso ; Drici, Abdelmalek ; Mingazzini, Tommaso | Springer | 2013-05-05The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control. They assume that the internal control is only time dependent. The proof relies on the ret[...]![]()
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Until now, an unconditional nonlinear energy stability analysis for thermal convection according to Navier–Stokes theory had not been developed for the case in which the viscosity depends on the temperature in a quadratic manner such that the vi[...]![]()
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We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is conside[...]![]()
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Conca, Carlos ; Díaz Díaz, Jesús Ildefonso ; Liñán, Amable ; Timofte, C. | Department of Mathematics Texas State University | 2004This paper concerns the homogenization of two nonlinear models for chemical reactive flows through the exterior of a domain containing periodically distributed reactive solid grains (or reactive obstacles). In the first model, the chemical react[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Gómez de Castro, Ana Inés ; Podol’skii, A. V. ; Shaposhnikova, T.A. | Maik Nauka-Interperiodica Publishing | 2016We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involvin[...]![]()
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This paper deals with the homogenization of a nonlinear problem modelllng chemical reactive flows through periodically perforated domains. The chemical reactions take place on the walls of the porous médium. The effective behavior of these react[...]![]()
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Casal, Alfonso C. ; Díaz Díaz, Jesús Ildefonso ; Stich, Michael ; Vegas Montaner, José Manuel | Springer | 2011We consider the complex Ginzburg-Landau equation with feedback control given by some delayed linear terms (possibly dependent of the past spatial average of the solution). We prove several bifurcation results by using the delay as parameter. We [...]![]()
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In this paper, we study the number of steady solutions of a non-linear model arising in Climatology. By applying a shooting method we show the existence of infinitely many steady solutions for some values of a parameter (the solar constant). Thi[...]![]()
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Mathematics plays a fundamental role in all scientific fields and, of course, in the Geosciences. This has been specially well known since, for example, the beginning of geodesy in the Greek era (VANÍC EK and KRAKIWSKY 1992) or in the pioneering[...]![]()
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We are concerned with the parabolic obstacle problem ut+Au+cu?f,u??, (ut+Au+cu?f)(u??)=0inQ=(0,T)×?, u=? on ?=(0,T)×??, u|t=0=u0 in ?, A being a linear elliptic second-order operator in divergence form or a nonlinear `pseudo-Laplacian'. We give [...]![]()
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In this paper, we are concerned with the parabolic obstacle problem (u(t)=partial derivative u/partial derivative t [GRAPHICS] (A is a linear second order elliptic operator in divergence form or a nonlinear "pseudo-Laplacian"). We give an isoper[...]![]()
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We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation u(t) - Delta u is an element of aH(u - mu) in Q = Omega X (0, T], where Omega subset of R(n) is a ring-shaped domain, a and mu are given positiv[...]![]()
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We study the dynamics and regularity of the level sets in solutions of the semilinear parabolic equation u(t) - Delta p(u) + f is an element of aH(u - mu) in Q = Omega x (0, T], P is an element of (1, infinity), where Omega subset of R(n) is a r[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Lazzo, Mónica ; Schmidt, Paul G. | Department of Mathematics. Texas State University | 2007This paper concerns the equation ?mu = |u| p, where m ? N, p ? (1, ?), and ? denotes the Laplace operator in RN, for some N ? N. Specifically, we are interested in the structure of the set L of all large radial solutions on the open unit ball B [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Lazzo, M. ; Schmidt, Paul G. | Society for Industrial and Applied Mathematics | 2005This paper is concerned with the elliptic system (0.1) Delta upsilon=phi, Delta phi=vertical bar del upsilon vertical bar(2) posed in a bounded domain Omega subset of R-N, N is an element of N. Specifically, we are interested in the existence an[...]![]()
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This paper is a study of some vanishing properties of weak solutions to nonlinear elliptic and parabolic equations. Instead of using monotonicity arguments, the method of proof is based on an energy method.![]()
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The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schrodinger equations, mainly the compactness of the support and its spatial localization. This question touches the very foundations underly[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Fowler, A.C. ; Muñoz, Ana Isabel ; Schiavi, E. | Birkhäuser | 2008-10-29The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and [...]![]()
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The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and [...]![]()
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The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Antontsev, S.N. | Real Academia Ciencias Exactas Físicas Y Naturales | 2007We study the boundary layer approximation of the, already classical, mathematical model which describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We start by proving the existence and uniqueness of solut[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Bermejo, R. ; Carpio, Jaime ; Tello, J. Ignacio | Pergamon-Elsevier Science Ltd | 2009-03The purpose of this paper is to carry out the mathematical and numerical analysis of a two-dimensional nonlinear parabolic problem on a compact Riemannian manifold without boundary, which arises in the energy balance for the averaged surface tem[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Stakgold, Ivar | Society for Industrial and Applied Mathematics | 1995-03When a diffusing gas reacts isothermally with an immobile solid phase, the resulting equations form a semilinear system consisting of a parabolic partial differential equation for the gas concentration coupled with an ordinary differential equat[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Stakgold, Ivar | Society for Industrial and Applied Mathematics | 1995-03When a diffusing gas reacts isothermally with an immobile solid phase, the resulting equations form a semilinear system consisting of a parabolic partial differential equation for the gas concentration coupled with an ordinary differential equat[...]![]()
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This paper deals with the study of some qualitative properties of solutions of mathematical models in non-Newtonian isothermal fluid flows and in theoretical glaciology. In the first type of models, we consider the extinction in a finite time of[...]![]()
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We study the boundary-layer approximation of the classical mathematical model that, describes the discharge of a, laminar hot gas in a stagnant colder atmosphere of the same gas. We prove the existence and uniqueness of solutions to a nondegener[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Padial Molina, Juan Francisco ; Rakotoson, Jean Michel Theresien | Pergamon-Elsevier Science | 1998The model studied concerns the case of a stellarator machine and the magnetic confinement is modeled by using averaging methods and suitable vacuum coordinates. This is shown to lead to a two-dimensional Grad-Shafranov type problem for the avera[...]![]()
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We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having[...]![]()
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We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having[...]![]()
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We consider a discretized a simple climate model of Sellers type and analyze the problem of transferring the system (through some sufficiently large time T) from a stationary state to another one in the same connected component.![]()
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We consider a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of the degenerate type. We derive some new L(1)-gradient type estimates for its solutions which are uniform in the sen[...]![]()
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New results are presented on the spatial and temporal localization of solutions of general nonlinear elliptic and parabolic equations in the presence of ``sources'' given by the right-hand side - the results are obtained by the energy method![]()
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We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, a[...]![]()
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We consider very weak solutions of a nonlinear version (non-Hookean materials) of the beam stationary Bernoulli-Euler equation, as well as the similar extension to plates, involving the bi-Laplacian operator, with Navier (hinged) boundary condit[...]![]()
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We study the qualitative behaviour of solutions of the equation ut?(um)xx+b?(u?)x=0 when it models some evaporation phenomena, ?![]()
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We study linear and nonlinear bilaplacian problems with hinged boundary conditions and right hand side in L1( : ?), with ? = dist(x, ?). More precisely, the existence and uniqueness of the very weak solution is obtained and some numerical techni[...]![]()
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We present some results on the mathematical treatment of a global twodimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature.[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Lerena, Belén ; Padial Molina, Juan Francisco ; Rakotoson, Jean Michel Theresien | Elsevier | 1999We prove the existence and the regularity of solutions of an elliptic-parabolic equation involving the notions of relative rearrangement and monotone rearrangement. These equations were obtained from 3D MHD systems, taking, (in particular) into [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Gómez Castro, David ; Shaposhnikova, Tatiana A. ; Zubova, Maria N. | Texas State University | 2019-06-04Our main interest in this article is the study of homogenized limit of a parabolic equation with a nonlinear dynamic boundary condition of the micro-scale model set on a domain with periodically place particles. We focus on the case of particles[...]![]()
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Recent studies on the mechanism governing the Laurentide ice sheet oscillations of the Last Ice Age focus on the most critical effect of the basal hydraulic processes enhanced when the ice is sliding along soft deformable beds. To understand the[...]![]()
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It is well-known that the pressure of a lubricating fluid filling the gap between two solid surfaces satisfies the Reynolds equation involving the distance function, h, between both planes, as a crucial coefficient. Nevertheless, in most of the [...]![]()
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We prove a pointwise gradient estimate for the solution of the Cauchy problem associated to the quasilinear Fisher-KPP type equation with a diffusion coefficient ?(u) satisfying that ?(0) = 0, ?(1) = 1 and a source term ?(u) which is vanishing o[...]![]()
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We study the longtime behavior of the solutions of a second order autonomous differential equation, differing from the one of a harmonic oscillator by a nonlinear friction term being only Hölder continuous. In particular, we show that there are [...]![]()
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This work deals with some numerical experiments regarding the distributed control of semilinear parabolic equations of the type y(t) - y(xx) + f (y) = u(Xw), in (0, 1) x (0, T), with Neumann and initial auxiliary conditions, where w is an open s[...]![]()
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The paper studies the approximate controllability for the Burgers equation. Due to the presence of a superlinear term, an obstruction phenomenon arises which implies a lack of approximate controllability in spaces of type L^p or $C$. However, th[...]![]()
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We obtain the existence of solutions of a two-dimensional free boundary problem modelling the magnetic confinement of a plasma in a Stellarator configuration. The nonlinear elliptic equation was obtained from the 3-D MHD system by Hender and Car[...]![]()
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In this communication, we consider the stationary problem of a non-linear parabolic system which arises in the context of dry-land vegetation. In the first part, we examine the existence and multiplicity of biomass stationary solutions, in terms[...]![]()
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We consider a mathematical model, posed by J.E. Scheinkman, simulating that an industrial project takes place into the environment without destroying it. We introduce a change of variable leading the formulation to a nonlinear evolution problem [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Díaz Díaz, Gregorio ; Otero Juez, Jesús | Amsterdam Elsevier Science 2000 | 2006-04We show the existence and uniqueness of a viscosity solution for an oblique nonlinear problem suggested by the study of the Backus problem on the determination of the external gravitational potential of the Earth from surface measurements of the[...]![]()
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"We consider some degenerate parabolic problems on a convex (or starshaped) ring. We prove that if the initial data have convex (or starshaped) level sets, then the solution u(t,?) has the same property for any positive t. Similar results are sh[...]![]()
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The authors present and study a problem which models the evolution of the ice sheet in the Laurentide. They consider a one-dimensional problem in (3-dimensional) space which involves three parameters: the ice thickness h , the amount of water fl[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Calvo, N. ; Durany, J. ; Schiavi, E. ; Vázquez, C. | Society for Industrial and Applied Mathematics | 2002This paper deals with the weak formulation of a free (moving) boundary problem arising in theoretical glaciology. Considering shallow ice sheet flow, we present the mathematical analysis and the numerical solution of the second order nonlinear d[...]![]()
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The fully nonlinear parabolic problem (P_{\text{}) u t =min{?,?u} for ?×R + , u=0 for ??×R + , u(x,0)=u 0 (x) for ? , occurs in some cases of Bellman's equation of dynamic programming. The author studies questions of asymptotic behavior[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Antontsev, S.N. | Real Academia Ciencias Exactas Físicas Y Naturales | 2009We prove several uniform L(1)-estimates on solutions of a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of degenerate type. They are uniform in the sense that they don't depend o[...]![]()
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We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging m[...]![]()
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The main result of the paper is the uniqueness of nonnegative solutions of the Cauchy problem and of the first and mixed boundary value problems for a class of degenerate parabolic equations which includes the model equation ut=(um)xx+(un)x, whe[...]![]()
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Díaz Díaz, Jesús Ildefonso ; De Thelin, Francois | Society for Industrial and Applied Mathematics | 1994This paper studies the Cauchy-Dirichlet problem associated with the equation b(u)t - div (\del u - K (b(u)) e\p-2 (del u - K (b(u))e)) + g (x, u) = f (t, x). This problem arises in the study of some turbulent regimes: flows of incompressible tur[...]![]()
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We consider the nonlinear Schrodinger equation associated to a singular potential of the form a vertical bar u vertical bar(-(1-m))u + bu, for some In is an element of (0, 1), on a possible unbounded domain. We use some suitable energy methods t[...]![]()
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This paper is a review of recent results (including the author's work) on a two-dimensional free-boundary problem, modeling magnetohydrodynamic equilibrium in a stellarator nuclear fusion device. The main tools used in the paper under review are[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Lerena Guil, María Belen ; Padial Molina, Juan Francisco | Elsevier Science Ltd | 2002An initial-boundary value problem for the nonlinear elliptic–parabolic equation (_(u))t ?_u = G(u)(t, x)+J(u)(t, x) is considered. Here _(s) = min(s, 0) = ?s?, G and J are nonlocal operators. This problem arises in the study of magnetic confinem[...]![]()
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We prove the existence and some qualitative properties of the solution to a two-dimensional free-boundary problem modeling the magnetic confinement of a plasma in a Stellarator configuration. The nonlinear elliptic partial differential equation [...]![]()
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We study the rigidification phenomenon for several thin slender bodies or shells, with a small curvature in the transversal direction to the main length, for which the propagation of singularities through the characteristics is of parabolic type[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Galiano, Gonzalo ; Jungel, Ansgar | Pergamon Elsevier Science Ltd | 1999-06-01The temporal and spatial localization of vacuum sets of the solutions to the drift-diffusion equations for semiconductors is studied in this paper. It is shown that if there are vacuum sets initially then there are vacuum sets for a small time, [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Galiano, Gonzalo ; Jungel, Ansgar | Pergamon Elsevier Science Ltd. | 2001-09This paper is about the drift-diffusion equations for semiconductors. Existence and uniqueness of weak solutions are obtained. The existence is proved by using the regularization technique. The proof of the uniqueness is interesting.![]()
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We study the rigidification phenomenon for several thin slender bodies or shells, with a small curvature in the transversal direction to the main length, for which the propagation of singularities through the characteristics is of parabolic type[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Padial Molina, Juan Francisco ; Rakotoson, Jean Michel Theresien | Cambridge University Press | 2007-09-18We consider some Bernoulli free boundary type problems for a general class of quasilinear elliptic (pseudomonotone) operators involving measures depending on unknown solutions. We treat those problems by applying the Ambrosetti-Rabinowitz minima[...]![]()
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It is known that several features of many react ion-diffusion systems can be studied through an associated Complex Ginzburg-Landau Equation (CGLE). In particular, the study of the catalytic CO oxidation leads to the Krischer-Eiswirth-Ertl model,[...]![]()
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We study the existence and uniqueness of solutions of a nonlinear stochastic pde proposed by R. North and R. F. Cahalan in 1982 for the modeling of non-deterministic variability (as, for instance, the volcano actions) in the framework of energy [...]![]()
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An ambiguity in the mathematical treatment of the study of bound state solutions of the Schrödinger equation for infinite well type potentials (studied for the first time in a pioneering article of 1928 by G. Gamow) is pointed out. An alternativ[...]![]()
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Sire prove the approximate controllability property for some higher order parabolic nonlinear equations of Cahn-Hilliard type when the nonlinearity is of sublinear type at infinity. We also give a counterexample showing that this property may fa[...]![]()
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In this communication we develop and improve some of the results of [4] on the approximate controllability of several semilinear parabolic boundary value problems where the nonlinear term appears either at the second order parabolic equation or [...]![]()
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We consider in this paper distributed systems governed by parabolic evolution equations which can blow up in finite time and which are controlled by initial conditions. We study here the following question : Can one choose the initial condition [...]![]()
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We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.![]()
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We show how the approximate controllability of nonlinear parabolic problems may fail although it is a well-known property for linear equations. For the case of the obstacle problem the answer depends on the negativeness of the righ hand side ter[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Liñán Martínez, Amable | Real Academia Ciencias Exactas Físicas Y Naturales | 2001We show that there are two curves of initial data (xo, vo) for which the solutions x(t) of the corresponding Cauchy problem associated to the equation xtt + |xí|a_1 xt + x — 0, where a G (0,1), vanish after a finite time. By using asymptotic and[...]![]()
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We prove the existence of a random global attractor for the multivalued random dynamical system associated to a nonlinear multivalued parabolic equation with a stochastic term of amplitude of the order of F. The equation was initially suggested [...]![]()
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The authors consider the Fokker-Planck equation ut=(um)xx+b(u?)x, x> 0, t> 0, with initial and boundary data u(x,0)=u0(x), x> 0, u(0,t)=u1(t), t> 0, u0 having its support in a bounded interval. They concentrate on the case 0![]()
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The Boussinesq system of hydrodynamics equations, arises from a zero order approximation to the coupling between the Navier-Stokes equations and the thermodynamic equation. The presence of density gradients in a fluid means that gravitational p[...]![]()
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We show how to stabilize the uniform oscillations of the complex Ginzburg-Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful [...]![]()
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This paper is devoted to a mathematical analysis of some general models of mass transport and other coupled physical processes developed in simultaneous flows of surface, soil and ground waters. Such models are widely used for forecasting (numer[...]![]()
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We study the differentiability of very weak solutions v is an element of L(1) (Omega) of (v, L* phi)(0) = (f, phi)(0) for all phi is an element of C(2)((Omega) over bar) vanishing at the boundary whenever f is in L(1) (Omega, delta), with delta [...]![]()
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The mathematical analysis of the shape of chemical reactors is studied in this paper through the research of the optimization of its effectiveness g such as introduced by R. Aris around 1960. Although our main motivation is the consideration of [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Hernández, Jesús | Society for Industrial and Applied Mathematics | 1984Let ??R N be a bounded smooth domain, f,g?C 1 (R) , ? 1 ,? 2 ?C 2 (??) , b,c?C 2 (R) nondecreasing, ?,?:R?2 R maximal monotone such that 0??(0)??(0) and consider the weakly coupled elliptic system (?) ?u??(u)f(v) , ??v??(u)g(v) on ? with[...]![]()
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We study a semilinear elliptic equation with a strong absorption term given by a non-Lipschitz function. The motivation is related with study of the linear Schrödinger equation with an infinite well potential. We start by proving a general exist[...]![]()
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Díaz Díaz, Gregorio ; Díaz Díaz, Jesús Ildefonso | American Institute of Mathematical Sciences | 2015-04This paper deals with several qualitative properties of solutions of some stationary equations associated to the Monge-Ampere operator on the set of convex functions which are not necessarily understood in a strict sense. Mainly, we focus our at[...]![]()
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We extend some previous local energy method to the study the free boundary generated by the solutions of quenching type parabolic problems involving a negative power of the unknown in the equation.![]()
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The aim of this paper is to study the asymptotic behavior of the solution of a transmission problem in some chemical reactive flows through periodically perforated domains. The domain is considered to be a fixed bounded open subset ??Rn, in whic[...]![]()
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We study the initial growth of the interfaces of non-negative local solutions of the equation u(t) = (u(m))xx - lambdau(q) when m greater-than-or-equal-to 1 and 0 [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Martin, Sébastien | Elsevier France-editions Scientifiques Medicales Elsevier | 2006-11We consider the Elrod-Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of [...]![]()
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We prove the convergence of the solutions for the incompressible homogeneous magnetohydrodynamics (MHD) system to the solutions to ideal MHD one in the inviscid and non-resistive limit, detailing the explicit convergence rates. For this study we[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Arjona, Alicia ; Fernández, José ; Rundle, J.B. | Birkhäuser | 2008-10-18In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the so[...]![]()
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We study the limit case corresponding to a model introduced by G.L. Stenchikov and A. Robock for the evolution of the temperature of an atmospheric column in absence of humidity. The model envolves a degenerate noncoercive quasilinear equation. [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Tello del Castillo, José Ignacio | Amsterdam Elsevier Science 2000 | 2003-03We study a model of growth of tumors with a free boundary delaying the tumor region. We take into account the presence of inhibitors and its interaction with the nutrients. We study the approximate controllability of the internal distribution of[...]![]()
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We analyze the sensitivity of a climatological model with respect to small changes in one of the distinguished parameters: the solar constant. We start by proving the stabilization of solutions of the evolution model when time tends to infinity.[...]![]()
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We present some recent results on the mathematical study of a global two-dimensional stationary climate model. We prove the multiplicity of solutions for some values of a solar parameter. Then, we obtain a S-shaped bifurcation branch.![]()
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We study the flat region of stationary points of the functional integral(Omega) F(|del u(x)|) dx under the constraint u 0 is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We con[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Mingazzini, Tomasso ; Ramos del Olmo, Ángel Manuel | American Institute of Mathematical Sciences | 2012We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The ne[...]![]()
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We study some retention phenomena on the free boundaries associated to some elliptic and parabolic problems of reaction-diffusion type. This is the case, for instance, of the wait in g time phenomenon for solutions of suitable parabolic equation[...]![]()
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In this comunication we present some results on the uniqueness and existence of BV solutions for the Cauchy-Dirichlet problem associated to the nonlinear diffusion equation b(u)(t) - div(\del u - k(b(u))e\(p-2)(del u - k(b(u))e)) + g(x,u) = f(t,[...]![]()
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We give sufficient conditions, being also necessary in many cases, for the existence of a periodic free boundary generated as the boundary of the support of the periodic solution of a general class of nonlinear parabolic equations. We show some [...]![]()
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We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions, The inverse problem arises in the modeling o[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Galiano, Gonzalo ; Padial Molina, Juan Francisco | Akademie Verlag GMBH | 1996We obtain the uniqueness of solutions of a nonlocal elliptic problem when the nonlinear terms at the right hand side are assumed to be prescribed. The problem arises in the study of the magnetic confinement of a plasma in a Stellarator device.![]()
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We get some necessary and sufficient conditions for the very weak solvability of the beam equation stated in terms of powers of the distance to the boundary, accordingly to the boundary condition under consideration. We get a L(1)-estimate by us[...]![]()
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Two problems arising in Environment are considered. The first one concerns a conjecture possed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the [...]![]()
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We use recent results by Diaz and Rakotoson concerning very weak solutions to linear boundary value problems in order to improve previous work on existence and properties of weak positive solutions to a model example of semilinear singular ellip[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Rakotoson, Jean Michel Theresien | American Institute of Mathematical Sciences | 2010-07We prove the existence of an appropriate function (very weak solution) u in the Lorentz space L(N') (,infinity)(Omega), N' = (N)(N - 1) satisfying Lu - Vu + g (x, u, del u) = mu in Omega an open bounded set of R(N), and u = 0 on partial derivati[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Rakotoson, Jean Michel Theresien ; Schmidt, Paul G. | Real Academia Ciencias Exactas Físicas Y Naturales | 2007We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regardin[...]![]()
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We prove a pointwise gradient estimate for the bounded weak solution of the Cauchy problem associated to the quasilinear Fisher-KPP type equation ut ='(u)xx + (u) when ' satisÖes that '(0)=0; and (u) is vanishing only for levels u = 0 and u = 1.[...]![]()
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We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Hernández, Jesús | Department of Mathematics Texas State University | 2014We give a survey of recent results and open problems concerning existence and multiplicity of positive and/or compact support solutions to some semilinear elliptic equations with singular nonlinear terms of absorption type. This includes the cas[...]![]()
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The countable branches of nodal solutions bifurcating from the infinity for a sublinear semilinear equation are described with two different approaches. In the one-dimensional case we use plane phase methods of ordinary differential equations. T[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Fleckinger-Pellé, Jacqueline | American Institute of Mathematical Sciences | 2004We study the positivity, for large time, of the solutions to the heat equation Q(a) (f,u(0)): [GRAPHIC] where Q is a smooth bounded domain in RN and a C R. We obtain some sufficient conditions for having a finite time t(p) > 0 (depending on a a[...]![]()
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In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this se[...]![]()
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In this paper we consider peculiar kinds of curved slender nearly cylindrical elastic shells enjoying rigidity properties inherited from the geometry which furnish remarkable properties of strength. In two previous papers were addressed the case[...]![]()
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In this paper we consider peculiar kinds of curved slender nearly cylindrical elastic shells enjoying rigidity properties inherited from the geometry which furnish remarkable properties of strength. In two previous papers were addressed the case[...]![]()
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We study the propagation of an initial disturbance u(0)(x) of an equilibrium state s epsilon R for the scalar conservation law u(t) + phi(u)(x) = 0 in (0, + infinity) x R. We give a necessary and sufficient condition on phi for the following pro[...]![]()
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Díaz Díaz, Jesús Ildefonso ; Glowinski, R. ; Guidoboni, G. ; Kim, T. | Real Academia Ciencias Exactas Físicas Y Naturales | 2010We study the transient flow of an isothermal and incompressible Bingham fluid. Similar models arise in completely different contexts as, for instance, in material science, image processing and differential geometry. For the two-dimensional flow [...]![]()
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We extend some previous existence results for quenching type parabolic problems involving a negative power of the unknown in the equation to the case of merely integrable initial data. We show that L1 ? is the suitable framework to obtain the co[...]![]()
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This paper deals with several qualitative properties of solutions of some stationary and parabolic equations associated to the Monge-Ampère operator. Mainly, we focus our attention in the occurrence of a free boundary (separating the region wher[...]![]()
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We study the global and non-global existence of solutions of degenerate singular parabolic equation with sources. In the case of global existence, we prove that any solution must vanish identically after a finite time if either the initial data [...]![]()
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Díaz Díaz, Jesús Ildefonso ; Arcoya Álvarez, David ; Tello del Castillo, José Ignacio | Elsevier | 1998-11-20In this paper we show the existence of a continuous and unbounded connected S-shaped set {(Q, u)} where Q is the solar constant and u satisfies a quasilinear eventually multivalued stationary equation on a Riemannian manifold without boundary ar[...]![]()
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Begout, Pascal ; Díaz Díaz, Jesús Ildefonso | Department of Mathematics Texas State University | 2014“Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires[...]![]()
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We prove the compactness of the support of the solution of some stationary Schrödinger equations with a singular nonlinear order term. We present here a sharper version of some energy methods previously used in the literature.![]()
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We prove the compactness of the support of the solution of some stationary Schrödinger equations with a singular nonlinear order term. We present here a sharper version of some energy methods previously used in the literature![]()
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This paper focuses upon the derivation of the similarity solutions of a nonlinear equation associated with a free boundary problem arising in glaciology. We present a potential symmetry analysis of this second order nonlinear degenerate paraboli[...]![]()
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A simple proof of the approximate controllability from the interior for nonlinear evolution problems
The approximate controllability property for solutions of a large class of nonlinear evolution problems is obtained under some abstract conditions which hold, for instance, when the control is the right hand side of the equation. Our very simple[...]![]()
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We study the existence, the asymptotic behaviour near the parabolic boundary and the uniqueness of the solutions of nonlinear reaction-diffusion equations, which blow up on the parabolic boundary. We extend some results for elliptic problems giv[...]![]()
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We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptoti[...]![]()
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In this survey we collect several results concerning S-type bifurcation curves for the number of solutions of reaction-diffusion stationary equations. In particular, we recall several results in the literature for the case of stationary energy b[...]![]()
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We study the approximate controllability property for y(t) - Delta phi(y) = u chi(omega), on Omega x (0, T), where Omega is a bounded open set of R-N and omega subset of Omega. First, we show some negative results for the case phi(s) = \s\(m-1)s[...]![]()
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Since the beginnings of the 1980s some energy methods have been introduced as an alternative to comparison principles in order to prove space and time localization of solutions of suitable nonlinear parabolic or elliptic equations. The study of [...]![]()
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A degenerate parabolic system consisting in two continuity equations for densities of charged particles and in the Poisson equation for an electric potential is considered. We show the finite speed of propagation, a waiting time property for the[...]![]()
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In this paper we consider the problem determined by the anti-plane shear dynamic deformations for the linear theory of viscoelasticity. First, we prove existence of solutions of the problem determined in a semi-infinite strip. Then, we show that[...]![]()
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The author studies the finite extinction time phenomenon in nonlinear evolution systems with dynamic boundary conditions and of Coulomb friction type problems. He gives some general results and methods and shows that this phenomenon is not a uni[...]