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Non-autonomous and random attractors for delay random semilinear equations without uniqueness

 

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Opened Access Non-autonomous and random attractors for delay random semilinear equations without uniqueness
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Author: Caraballo Garrido, Tomás
Garrido Atienza, María José
Schmalfuss, Björn
Valero Cuadra, José
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2008
Published in: Discrete and Continuous Dynamical Systems, 21(2), 415-443
Document type: Article
Abstract: We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and random dynamical systems. The standard assumption of compactness of these systems can be replaced by the assumption of asymptotic compactness. Then, we apply the abstract theory to handle a random reaction-diffusion equation with memory or delay terms which can be considered on the complete past defined by R−.In particular, we do not assume the uniqueness of solutions of these equations.
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URI: http://hdl.handle.net/11441/23681

DOI: http://dx.doi.org/10.3934/dcds.2008.21.415

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