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Article
Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs
(World Scientific Publishing, 2005-08)
In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut − ∆u = λu − b(t)u 2 with b(t) ∈ [b0, B0], 0 < b0 < B0 < 2b0. In particular, we prove the ...
Article
Existence and uniqueness of solutions for delay stochastic evolution equations of second order in time
(World Scientific Publishing, 2003-06)
We prove some results on the existence and uniqueness of solutions for a class of evolution equations of second order in time, containing some hereditary characteristics. Our theory is developed from a variational point ...
Article
Asymptotic behavior of nonlinear elliptic systems on varying domains
(Society for Industrial and Applied Mathematics, 2000)
We consider a monotone operator of the form Au = −div(a(x, Du)), with Ω ⊆ Rn and a : Ω×MM×N → MM×N , acting on W1,p 0 (Ω, RM). For every sequence (Ωh) of open subsets of Ω and for every f ∈ W−1,p0 (Ω, RM), 1/p+ 1/p0 = 1, ...
Article
Asymptotic Behaviour of Monotone Multi-Valued Dynamical Systems
(2005)
We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by the applications in the theory of di¤erential equations without uniqueness of solutions. For an order ...
Article
Sistemas dinámicos estocásticos no autónomos y sistemas multivaluados
(Sociedad Española de Matemática Aplicada, 2002)
Uno de los conceptos más importantes para la descripción del comportamiento asintótico de ecuaciones en derivadas parciales de evolución disipativas es el de atractor global. Presentamos los trabajos realizados en esta ...
Article
On the existence and multiplicity of positive solutions for some indefinite nonlinear eigenvalue problem
(American Mathematical Society, 2004-06)
This paper concerns with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation method to ...
Article
Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations
(2005)
An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white noise is considered. The system models temperature dependent or heat generating wave phenomena in a ...
Article
An optimal control problem for a generalized Boussinesq model: The time dependent case
(Universidad Complutense de Madrid, 2007)
We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq ...
Presentation
Article
A gradient-like non autonomous evolution process
(2009)
In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ½ Rn with Dirichlet boundary conditions, where f is a ...