Stability and random attractors for a reaction-diffusion equation with multiplicative noise

Tomás Caraballo; José A. Langa; James C. Robinson

doi:10.3934/dcds.2000.6.875

Article Contents

2000, Volume 6, Issue 4: 875-892. Doi: 10.3934/dcds.2000.6.875

This issue Previous Article A topological degree approach to sublinear systems of second order differential equations Next Article The set of periods for a class of skew-products

Stability and random attractors for a reaction-diffusion equation with multiplicative noise

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
Mathematics Institute, University of Warwick, Coventry CV4 7AL

Received: June 30, 1999

Revised: June 30, 2000

Published: September 2000

Abstract Related Papers Cited by

Abstract

We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white noise (in the sense of Itô) stabilizes the stationary solution $x\equiv 0$. We show in addition that this stochastic equation has a finite-dimensional random attractor, and from our results conjecture a possible bifurcation scenario.

Keywords:

Mathematics Subject Classification: 35B40, 35K57, 58F12, 60H15.

Citation:

Article Metrics

HTML views() PDF downloads(169) Cited by(0)

Stability and random attractors for a reaction-diffusion equation with multiplicative noise

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Stability and random attractors for a reaction-diffusion equation with multiplicative noise

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content