Article
Gradient Infinite-Dimensional Random Dynamical Systems
Author/s | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Liu, Zenxhin |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2012 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | In this paper we introduce the concept of a gradient random dynamical system as a random semiflow
possessing a continuous random Lyapunov function which describes the asymptotic regime of the
system. Thus, we are able ... In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic regime of the system. Thus, we are able to analyze the dynamical properties on a random attractor described by its Morse decomposition for infinite-dimensional random dynamical systems. In particular, if a random attractor is characterized by a family of invariant random compact sets, we show the equivalence among the asymptotic stability of this family, the Morse decomposition of the random attractor, and the existence of a random Lyapunov function. |
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