Exponential attractors for random dynamical systems and applications

The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-d...

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Bibliographic Details
Main Authors Shirikyan, Armen, Zelik, Sergey
Format Journal Article
LanguageEnglish
Published 16.08.2012
Subjects
Mathematics - Analysis of PDEs
Mathematics - Dynamical Systems
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Summary:The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction-diffusion system with a random perturbation. We show, in particular, that the attractors can be constructed in such a way that the symmetric distance between the attractors for stochastic and deterministic problems goes to zero with the amplitude of the random perturbation.
DOI:10.48550/arxiv.1208.3361