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

Authors
Caraballo, T Langa, JA Robinson, JC
Citation
T. Caraballo et al., Stability and random attractors for a reaction-diffusion equation with multiplicative noise, DISCR C D S, 6(4), 2000, pp. 875-892
Citations number
33
Categorie Soggetti
Mathematics
Journal title
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN journal
10780947 → ACNP
Volume
6
Issue
4
Year of publication
2000
Pages
875 - 892
Database
ISI
SICI code
1078-0947(200010)6:4<875:SARAFA>2.0.ZU;2-T
Abstract
We study the asymptotic behaviour of a reaction-diffusion equation, and pro ve that the addition of multiplicative white noise (in the sense of It (o) over cap) stabilizes the stationary solution x = 0. We show in addition tha t this stochastic equation has a finite-dimensional random attractor, and f rom our results conjecture a possible bifurcation scenario.