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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 [...]