The exponential stability of neutral stochastic delay partial differential equations

Tomás Caraballo; José Real; T. Taniguchi

doi:10.3934/dcds.2007.18.295

Article Contents

2007, Volume 18, Issue 2&3: 295-313. Doi: 10.3934/dcds.2007.18.295

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The exponential stability of neutral stochastic delay partial differential equations

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

Received: November 30, 2005

Revised: April 30, 2006

Published: May 2007

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Abstract

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:

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

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

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