The exponential stability of neutral stochastic delay partial differential equations

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February & March 2007, 18(2&3): 295-313. doi: 10.3934/dcds.2007.18.295

The exponential stability of neutral stochastic delay partial differential equations

Tomás Caraballo ^1, , José Real ^2, and T. Taniguchi ^3,

1.	Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.	Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
3.	Division of Mathematical Sciences, Graduate School of Comparative Culture, Kurume University, Miimachi, Kurume, Fukuoka 839-8502, Japan

Received December 2005 Revised May 2006 Published March 2007

Abstract
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In this paper we analyze the almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations. These kind of equations arise in problems related to coupled oscillators in a noisy environment, or in viscoeslastic materials under random or stochastic influences.

Keywords: existence of solutions, exponential stability., ultimate boundedness, Neutral stochastic partial differential equations.

Mathematics Subject Classification: Primary: 60H20; Secondary: 60G48.

Citation: Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295

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