Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions, so that uniquene...

Descripción completa

Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Morillas, F., Valero, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/138663
Acceso en línea:https://hdl.handle.net/11441/138663
https://doi.org/10.1016/j.jde.2012.03.020
Access Level:acceso abierto
Palabra clave:Stochastic lattice differential equations
Random attractors
Multiplicative noise
Set-valued dynamical system
Descripción
Sumario:In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative 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