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Autor Rodríguez Bernal, Aníbal |
Documentos disponibles escritos por este autor (73)
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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[...]texto impreso
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[...]texto impreso
We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in L-q(Omega) for each 1texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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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), 1texto impreso
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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 [...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]