Invariant foliations for stochastic partial differential equations with non-dense domain

Abstract

In this paper we study the existence of Lipschitz invariant stable and unstable foliations for a class of stochastic partial differential equations with non-dense domain. We would like to emphasize that the linear part neither generates a C 0 C_0 semigroup nor satisfies the Hille-Yosida condition. Using the theory of integrated semigroup and Lyapunov-Perron method, we establish the main result to trace the long-term behavior of such an equation and apply it to a stochastic parabolic equation.