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The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model
(Sociedad Española de Matemática Aplicada, 2010)
In 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 ...
Artículo
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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 ...
Artículo
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Stability results for neutral stochastic functional differential equations via fixed point methods
(Taylor and Francis, 2020)
In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and ...
Artículo
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Analysis of a coupled fluid-structure model with applications to hemodynamics
(Society for Industrial and Applied Mathematics, 2016)
We propose and analyze a simplified fluid-structure coupled model for flows with compliant walls. As in [F. Nobile and C. Vergara, SIAM J. Sci. Comput., 30 (2008), pp. 731-763], the wall reaction to the fluid is modeled ...
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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 ...
Artículo
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Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
(Springer Verlag (Germany), 2011)
Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively ...
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On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal
(SIAM, 2021-08-05)
In this paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the ...
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Statistical solutions and Kolmogorov entropy for the lattice long-wave-short-wave resonance equations in weighted space
(Elsevier, 2023-04-25)
This article studies the lattice long-wave-short-wave resonance equations in weighted spaces. The authors first prove the global well-posedness of the initial value problem and the existence of the pullback attractor for ...
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Analysis of a stochastic 2D–Navier-Stokes model with infinite delay
(Springer, 2019-12)
Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics are established. The existence and uniqueness of solutions in the case of unbounded (infinite) delay ...
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Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution
(American Institute of Mathematical Sciences, 2017-07)
In this paper, the existence of solution for a p-Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal ...