Stability and convergence via Lyapunov-like functionals of Stochastic parabolic partial differential equations

In this paper, we employ comparison principle and Lyapunov-like functional techniques to study the convergence and stability behaviour of diffusion systems in a random environment. The system is modelled using the Ito-type stochastic parabolic partial differential equations. Sufficient conditions for various concepts of stability and convergence such as the pth moment, in probability, and asymptotic stability of the solution process of the system are obtained. These sufficient conditions are based on the M-matrix tests including the diagonal dominance which are well known for its robustness implications. Moreover, an example is provided to illustrate the significance of the presented results. (C) 2003 Elsevier Inc. All rights reserved.