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

We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white noise (in the sense of Itˆo) stabilizes the stationary solution x 0. We show in addition that this stochastic equation has a finite-dimensional random attractor, and from our resul...

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Detalhes bibliográficos
Autores: Caraballo Garrido, Tomás, Langa Rosado, José Antonio, Robinson, James C.
Formato: artículo
Fecha de publicación:2000
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23712
Acesso em linha:http://hdl.handle.net/11441/23712
https://doi.org/10.3934/dcds.2000.6.875
Access Level:acceso abierto
Palavra-chave:Random attractors
Hausdorff dimension
stochastic stabilization
Chafee-Infante equation
Descrição
Resumo:We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white noise (in the sense of Itˆo) stabilizes the stationary solution x 0. We show in addition that this stochastic equation has a finite-dimensional random attractor, and from our results conjecture a possible bifurcation scenario.