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Artículo
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Non-Autonomous Attractor for Integro-Differential Evolution Equations
(2009)
We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an ...
Artículo
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Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations
(2006)
In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers the stochastic term in the Ito or Stratonovich sense. In particular, we prove that the Stratonovich ...
Artículo
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Stochastic Functional Partial Differential Equations: Existence, Uniqueness and Asymptotic Decay Property
(2000)
Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces are established. Suf cient conditions which guarantee the transference of mean square and pathwise ...
Artículo
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Attractors for Stochastic Lattice Dynamical Systems with a Multiplicative Noise
(2008)
In this paper, we consider a stochastic lattice di®erential equation with di®usive nearest neighbor interaction, a dissipative nonlinear reaction term, and a multiplicative white noise at each node. We prove the existence ...
Artículo
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Invariant Measures and Statistical Solutions of the Globally Modified Navier-Stokes Equations
(2008)
We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, and we investigate the relationship between global attractors, invariant measures, time-average ...
Tesis Doctoral
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Existencia, unicidad y comportamiento asintótico en algunos sistemas dinámicos deterministas y estocásticos
(2003-05-23)
La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la Teoría de Atractores. Más concretamente, en el primer bloque de la tesis se presentan resultados ...
Artículo
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Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
(2004)
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution ...
Artículo
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Recent results on stabilization of PDEs by noise
(Sociedad Española de Matemática Aplicada, 2006-12)
This paper is intended to be a brief review on some recent results on the stabilization effect produced by noise in phenomena modelled by partial differential equations. We emphasyse the different effects that distinct ...
Artículo
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Stabilization of Stationary Solutions of Evolution Equations by Noise
(2006)
We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic semilinear evolution equations. Our main result shows, in particular, that noise can have a stabilization ...
Artículo
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The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations
(2006)
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise ...