CENTER MANIFOLDS FOR ILL-POSED STOCHASTIC EVOLUTION EQUATIONS

The aim of this paper is to develop a center manifold theory for a class of stochastic partial differential equations with a non-dense domain through the Lyapunov-Perron method. We construct a novel variation of constants formula by the resolvent operator to formulate the integrated solutions. Moreover, we impose an additional condition involving a non-decreasing map to deduce the required estimate since Young's convolution inequality is not applicable. As an application, we present a stochastic parabolic equation to illustrate the obtained results.

Automated summary

The aim of this paper is to develop a center manifold theory for a class of stochastic partial differential equations with a non-dense domain using the Lyapunov-Perron method and the resolvent operator to construct a novel variation of constants formula. An additional condition involving a non-decreasing map is imposed to deduce the required estimate, as Young's convolution inequality is not applicable. As an application, a stochastic parabolic equation is presented to illustrate the obtained results.