Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities |
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| Authors: | Tomás Caraballo F Morillas J Valero |
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| Institution: | 1. Depto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080 Sevilla, Spain;2. Universitat de València, Departament d?Economia Aplicada, Facultat d?Economia, Campus dels Tarongers s/n, 46022 València, Spain;3. Universidad Miguel Hernández, Centro de Investigación Operativa, Avda. Universidad s/n, Elche (Alicante) 03202, Spain |
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| Abstract: | 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. |
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