Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory

Tomás Caraballo; I. D. Chueshov; Pedro Marín-Rubio; José Real

doi:10.3934/dcds.2007.18.253

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2007, Volume 18, Issue 2&3: 253-270. Doi: 10.3934/dcds.2007.18.253

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Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov
3.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received: March 2006

Revised: May 2006

Published: June 2007

Abstract / Introduction Related Papers Cited by

Abstract

The existence and uniqueness of solutions for a stochastic reaction-diffusion equation with infinite delay is proved. Sufficient conditions ensuring stability of the zero solution are provided and a possibility of stabilization by noise of the deterministic counterpart of the model is studied.

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Mathematics Subject Classification: Primary: 60H15, 35K40.

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