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–diffus...

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Bibliographic Details
Published inStochastic partial differential equations : analysis and computations Vol. 1; no. 2; pp. 241 - 281
Main Authors Shirikyan, Armen, Zelik, Sergey
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2013
Subjects
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematics
Mathematics and Statistics
Numerical Analysis
Partial Differential Equations
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Reaction-diffusion equation
35R60
Random exponential attractors
35B41
35K57
60H15
Stochastic PDE’s
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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.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-013-0007-1