Article
The dimension of attractors of nonautonomous partial differential equations
Author/s | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Valero Cuadra, José |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2003 |
Deposit Date | 2015-04-08 |
Published in |
|
Abstract | 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. |
Files | Size | Format | View | Description |
---|---|---|---|---|
file_1.pdf | 207.9Kb | [PDF] | View/ | |