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March  2007, 18(2&3): 253-270. doi: 10.3934/dcds.2007.18.253

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

Tomás Caraballo 1, , I. D. Chueshov 2, , Pedro Marín-Rubio 1, and  José Real 3,

1. 

Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain
2. 

Department of Mechanics and Mathematics, Kharkov National University, 4 Svobody sq., 61077, Kharkov, Ukraine
3. 

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received  March 2006 Revised  May 2006 Published  March 2007

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.
Keywords: materials with memory, stabilization., mean square exponential stability, Stochastic heat equation.
Mathematics Subject Classification: Primary: 60H15, 35K4.
Citation: Tomás Caraballo, I. D. Chueshov, Pedro Marín-Rubio, José Real. Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 253-270. doi: 10.3934/dcds.2007.18.253
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