Small random perturbations of a dynamical system with blow-up

We study small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and as...

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Detalhes bibliográficos
Autores: Groisman, Pablo Jose, Saglietti, Santiago Juan
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/19945
Acesso em linha:http://hdl.handle.net/11336/19945
Access Level:acceso abierto
Palavra-chave:Blow-Up
Metastability
Stochastic Differential Equations
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:We study small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.