Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications

Abstract

This paper derives several wellposedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both statedependent and additive stochastic disturbances. These systems do not need to satisfy global Lipschitz and linear growth conditions. First, the nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in appropriate Hilbert spaces, using functional analysis. Second, Lyapunov sufficient conditions are derived to ensure wellposedness and almost sure (a.s.) asymptotic and practical stability of strong solutions. Third, the above results are applied to study wellposedness and stability of the solutions of two exemplary SDPSs.