Lower and Upper Bounds of the Explosion Time of a Reaction-Diffusion System Perturbed by Brownian Motion

We investigate lower and upper bounds for the blow-up time of a system of semilinear stochastic partial differential equations (SPDEs). From these bounds we obtain lower and upper bounds for the probability of explosion in finite time of the system. The lower bound is obtained from a related system...

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Detalles Bibliográficos
Autor: JOSE ALFREDO LOPEZ MIMBELA
Tipo de recurso: informe técnico
Estado:Versión publicada
Fecha de publicación:2015
País:México
Institución:Centro de Investigación en Matemáticas
Repositorio:Repositorio Institucional CIMAT
Idioma:inglés
OAI Identifier:oai:cimat.repositorioinstitucional.mx:1008/584
Acceso en línea:http://cimat.repositorioinstitucional.mx/jspui/handle/1008/584
Access Level:acceso abierto
Palabra clave:info:eu-repo/classification/MSC/Movimiento Browniano
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120803
Descripción
Sumario:We investigate lower and upper bounds for the blow-up time of a system of semilinear stochastic partial differential equations (SPDEs). From these bounds we obtain lower and upper bounds for the probability of explosion in finite time of the system. The lower bound is obtained from a related system of random partial differential equations, and is given in terms of the Laplace transform of a perpetual integral functional of a standard Brownian motion. The upper bound is given in terms of the expected value of a similar perpetual integral functional. We also extend the approach introduced by Chow (2011) to our system of SPDEs, and get an explosion result in Lp-norm, for any 1< p < Infinito.