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

作者：Caraballo Tomas; Morillas F; Valero J^*

来源：Journal of Differential Equations, 2012, 253(2): 667-693.

DOI：10.1016/j.jde.2012.03.020

• Stochastic lattice differential equations
• Random attractors
• Multiplicative noise
• Set-valued dynamical system

In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative noise. %26lt;br%26gt;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. %26lt;br%26gt;Using the theory of multi-valued random dynamical systems we prove the existence of a random compact global attractor.

• 出版日期2012-7-15