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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

 

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Opened Access Random attractors for stochastic lattice systems with non-Lipschitz non-linearity
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Author: Caraballo Garrido, Tomás
Morillas Jurado, Francisco
Valero Cuadra, José
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2012
Published in: Journal of Difference Equations and Applications, 75(14), 5702-5722
Document type: Article
Abstract: In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.
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URI: http://hdl.handle.net/11441/23708

DOI: http://dx.doi.org/10.1080/10236198.2010.549010

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