Random pullback exponential attractors: General existence results for random dynamical systems in Banach spaces

Tomás Caraballo; Stefanie Sonner

doi:10.3934/dcds.2017277

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2017, Volume 37, Issue 12: 6383-6403. Doi: 10.3934/dcds.2017277

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Random pullback exponential attractors: General existence results for random dynamical systems in Banach spaces

Tomás Caraballo^1, and
Stefanie Sonner^2, ,

1.
Departamento Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, C/ Tarfia s/n, 41012 Sevilla, Spain
2.
Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstr. 36, 8010 Graz, Austria

* Corresponding author: Stefanie Sonner
* Corresponding author: Stefanie Sonner

Received: February 28, 2017

Revised: June 30, 2017

Published: October 2017

The first author was partially supported by FEDER (EU) and Ministerio de Economía y Competitividad (Spain) grant MTM2015-63723-P and by the Junta de Andalucía under the Proyecto de Excelencia P12-FQM-1492.

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Abstract

We derive general existence theorems for random pullback exponential attractors and deduce explicit bounds for their fractal dimension. The results are formulated for asymptotically compact random dynamical systems in Banach spaces.

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Mathematics Subject Classification: Primary: 37L30, 37L55; Secondary: 35R60, 37B40.

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References

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