Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 429568, 13 pages
http://dx.doi.org/10.1155/2012/429568
Research Article

Stability of Stochastic Reaction-Diffusion Systems with Markovian Switching and Impulsive Perturbations

Yanbo Li1,2 and Yonggui Kao1

1Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
2School of Mathematical Sciences, Guangxi Teachers Education University, Guangxi 530001, China

Received 4 September 2012; Accepted 23 September 2012

Academic Editor: Alexei Mailybaev

Copyright © 2012 Yanbo Li and Yonggui Kao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to investigating mean square stability of a class of stochastic reaction-diffusion systems with Markovian switching and impulsive perturbations. Based on Lyapunov functions and stochastic analysis method, some new criteria are established. Moreover, a class of semilinear stochastic impulsive reaction-diffusion differential equations with Markovian switching is discussed and a numerical example is presented to show the effectiveness of the obtained results.