Abstract
In this article, 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.
Acknowledgements
This work was partially supported by Spanish Ministerio de Ciencia e Innovación, Projects MTM2008-00088 and MTM2009-11820, the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía), Proyecto de Excelencia P07-FQM-02468 and the Consejería de Cultura y Educación (Comunidad Autónoma de Murcia), grant 08667/PI/08.