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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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In this paper we show that dissipative reaction-diffusion equations in unbounded domains posses extremal semistable ground states equilibria, which bound asymptotically the global dynamics. Uniqueness of such positive ground state and their appr[...]texto impreso
We make precise the sense in which spatial homogenization to a constant function in space is attained in a linear parabolic problem when large diffusion in all parts of the domain is assumed. Also interaction between diffusion and boundary flux [...]texto impreso
We analyze the asymptotic behavior of the attractors of a parabolic problem when some reaction and potential terms are concentrated in a neighborhood of a portion ? of the boundary and this neighborhood shrinks to ? as a parameter ? goes to zero[...]texto impreso
In this paper we consider linear parabolic problems when some reaction and potential terms are concentrated in a neighborhood of a portion I" of the boundary. This neighborhood shrinks to I" as a parameter epsilon goes to zero. Then we derive th[...]texto impreso
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We solve some fourth order parabolic equations, obtained from perturbations of the parabolic bi-Laplacian equation, with special focus on smoothing estimates. Several classes of initial data are considered including data in Lebesgue and Bessel-L[...]texto impreso
Starting form basic principles, we obtain mathematical models that describe the traffic of material objects in a network represented by a graph. We analyze existence, uniqueness, and positivity of solutions for some implicit models. Also, some l[...]texto impreso
In this paper we survey some recent results on the behavior of solutions of parabolic equations subjected to nonlinear boundary conditions. The results range from local existence and regularity of solutions, to global existence, dissipativeness [...]texto impreso
We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these sol[...]texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Rossi, Julio D. | Cambridge University Press | 2008In this paper we prove that the best constant in the Sobolev trace embedding H1() ,! Lq(@) in a bounded smooth domain can be obtained as the limit as " ! 0 of the best constant of the usual Sobolev embedding H1() ,! Lq(!", dx/") where !" = {x 2 [...]texto impreso
In this paper we address the well posedness of the linear heat equation under general periodic boundary conditions in several settings depending on the properties of the initial data. We develop an Lq theory not based on separation of variables [...]texto impreso
Langa, J.A. ; Rodríguez Bernal, Aníbal ; Suárez, Antonio | Sociedad Española de Matemática Aplicada | 2010In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution[...]texto impreso
Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Rodríguez Bernal, Aníbal | Elsevier | 2000-11-20The motivations to study the problem considered in this paper come from the theory of composite materials, where the heat diffusion properties can change from one part of the domain to another. Mathematically, this leads to a nonlinear second-or[...]