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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under som[...]![]()
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Arrieta Algarra, José María ; Carvalho, Alexandre N. ; Rodríguez Bernal, Aníbal | Elsevier | 1999-08-10We prove existence, uniqueness and regularity of solutions For heat equations with nonlinear boundary conditions. We study these problems with initial data in L-q(Omega), W-1,W-q(Omega), 1![]()
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Rodríguez Bernal, Aníbal ; Langa, José A. ; Robinson, James C. ; Suárez, Antonio | Society for Industrial and Applied Mathematics | 2009Lotka–Volterra systems are the canonical ecological models used to analyze population dynamics of competition, symbiosis, or prey-predator behavior involving different interacting species in a fixed habitat. Much of the work on these models has [...]![]()
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We study linear perturbations of analytic semigroups defined on a scale of Banach spaces. Fitting the action of the linear perturbation between two spaces of the scale determines the spaces of existence and regularity of solutions for the pertur[...]![]()
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Let $\Omega$ be a bounded domain in a Euclidean space, with a smooth boundary. The paper deals with the linear non-autonomous model equation $$ u_t-\Delta u=C(t,x) \quad (x\in \Omega,\ t> 0), $$ where $C(x,t)$ is a given function. Besides, vario[...]![]()
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We analyse the dynamics of the non-autonomous nonlinear reaction–diffusion equation ut ?_u = f (t,x,u), subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our mai[...]![]()
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In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstra[...]![]()
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We solve second order parabolic equations with nonsmooth coefficients and initial data in suitable uniform spaces. We also show the smoothing effect of the corresponding analytic semigroup depending on the integrability properties of the coeffic[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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 [...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]