Artículo
The dimension of attractors of nonautonomous partial differential equations
Autor/es | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Valero Cuadra, José |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2003 |
Fecha de depósito | 2015-04-08 |
Publicado en |
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Resumen | The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of general nonautonomous partial differential equations. This is a time-dependent family of compact ... The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of general nonautonomous partial differential equations. This is a time-dependent family of compact sets, invariant for the associated process and attracting “from ¡1”: In general, the concept is rather different from the classical one of global attractor for autonomous dynamical systems. We prove a general result on the finite fractal dimensionality of each compact set of this family. In this way, we generalize previous results of Chepyzhov and Vishik in [6]. Our results are also applied to differential equations with a nonlinear term having polynomial growth at most. |
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