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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Caraballo, Tomas²  Morillas, F.³  Valero, J.¹ 

[1] Univ Miguel Hernandez, Ctr Invest Operat, Avda Univ S-N, Elche 03202, Alicante, Spain

[2] Univ Seville, Depto Ecuac Diferenciales & Anal Numer, E-41080 Seville, Spain

[3] Univ Valencia, Fac Econ, Dept Econ Aplicada, Valencia 46022, Spain

关键词: Stochastic lattice differential equations;    Random attractors;    Multiplicative noise;    Set-valued dynamical system;   

DOI  :  10.1016/j.jde.2012.03.020

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free