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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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Rodríguez Bernal, Aníbal ; Vidal López, Alejandro | American Institute of Mathematical Sciences | 2007We give conditions for the existence of a unique positive complete trajectories for non-autonomous reaction-diffusion equations. Also, attraction properties of the unique complete trajectory is obtained in a pullback sense and also forward in ti[...]![]()
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The authors find a growth condition on the nonlinear term f(x, u) of a nonlinear heat equation which ensures the existence of maximal and minimal equilibria that bound asymptotically all solutions to that nonlinear heat equation.![]()
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We consider a reaction diffusion equation u(t) = Delta u + f(x, u) in R-N with initial data in the locally uniform space (L) over dot(U)(q)(R-N), q is an element of [1, infinity), and with dissipative nonlinearities satisfying sf(x, s) N/2. U[...]![]()
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In this well-written paper, the authors consider monotone semigroups in ordered spaces and give general results concerning the existence of extremal equilibria and global attractors. \par In the first part of the paper, some notions concerning d[...]![]()
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We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and[...]![]()
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We analyse the dynamics of a fluid transporting a soluble substance in the interior of a closed loop of arbitrary geometry and subjected to the action of gravity and natural convection. After obtaining the governing equations and analysing the w[...]![]()
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Arrieta Algarra, José María ; Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | World Scientific Publ Co Pte Ltd | 2005We analyze the limit of solutions of an elliptic problem, with zero flux boundary conditions when the reaction terms are concentrated in a neighborhood of the boundary and that shrinks to the boundary as a parameter goes to zero. We prove that t[...]![]()
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Arrieta Algarra, José María ; Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | Universidad Autónoma Madrid | 2008We analyze the limit of the solutions of an elliptic problem when some reaction and potential terms are concentrated in a neighborhood of a portion Gamma of the boundary and this neighborhood shrinks to Gamma as a parameter goes to zero. We prov[...]![]()
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Arrieta Algarra, José María ; Pardo San Gil, Rosa María ; Rodríguez Bernal, Aníbal | World Scientific Publishing | 2010Summary: "We consider an elliptic equation ??u+u=0 with nonlinear boundary conditions ?u/?n=?u+g(?,x,u) , where (g(?,x,s))/s?0 as |s|?? . In [Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 225--252; MR2360769 (2009d:35194); J. Differentia[...]![]()
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In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1![]()
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Linear 2m-th order uniformly elliptic operators are shown to generate semigroups of bounded linear operators with suitable smoothing properties in scales of locally uniform Bessel's and Lebesgue's spaces.![]()
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The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ?N, graphs, manifolds, multi-structures and some fractal sets. For this, [...]![]()
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Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Cholewa, Jan W. ; Dlotko, Tomasz | World Scientific | 2004We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp L-p - L-q-type estimates in uniform spaces for heat and Schrodinger semigroups and analyze the regularizing effect and the exponential type of these semigroup[...]![]()
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We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable[...]![]()
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In this work we analyze the existence of solutions that blow-up in finite time for a reaction-diffusion equation ut??u=f(x,u) in a smooth domain ? with nonlinear boundary conditions ?u?n=g(x,u). We show that, if locally around some point of the [...]![]()
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Arrieta Algarra, José M. ; Pardo, Rosa ; Rodríguez Bernal, Aníbal | Department of Mathematics Texas State University | 2014We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonl[...]![]()
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We analyze singular perturbations in elliptic equations, subjected to various boundary conditions, in which the diffusion is going to infinity in localized regions inside the domain and therefore solutions undergo a localized spatial homogenizat[...]![]()
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We study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations. A priori, we review both local and global dynamics of the system [...]![]()
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Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal | World Scientific Publ. Co. Pte. Ltd. | 2004-10In this paper we show that several known critical exponents for nonlinear parabolic problems axe optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and C[...]![]()
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The authors consider a reaction-diffusion equation in a bounded smooth domain ??R n with nonlinear flux terms on the boundary of ? . They derive suitable conditions on the nonlinear terms of the problem which imply its dissipativity. The autho[...]![]()
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Cholewa, Jan W. ; Rodríguez Bernal, Aníbal | Institute of Mathematics, Academy of Sciences of the Czech Republic | 2014We consider the Cahn-Hilliard equation in H1(RN ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as |u| ? ? and logistic type nonlinearities. In both situations we prove the H2(RN )-bound[...]![]()
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We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in L-q(Omega) for each 1![]()
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In this paper we analyse a singular perturbation problem for linear wave equations with interior and boundary damping. We show how the solutions converge to the formal parabolic limit problem with dynamic boundary conditions. Conditions are give[...]![]()
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We prove that compact attractors of nonlinear parabolic problems with general potentials have finite fractal and Haussdorf dimension. The linear potentials belong to the space of locally uniform functions in and, unlike other references, they a[...]