Invariant Manifolds For SPDEs In Varying Phase Spaces

In this thesis we investigate the limiting behavior of invariant manifolds for a class of stochastic partial differential equations with additive noise in different phase spaces.First,we show that solutions of stochastic partial differential equations define a random dynamical system by the random transformation,and study the existence and smoothness of the center manifolds.Further,we obtain the Lipschitz convergence and smooth convergence of the center manifolds when the phase spaces approach to their singular limit.Then we prove the existence and smoothness of the center-unstable manifolds by the stationary solutions,and study the convergence of the invariant manifolds.Finally,we give an example to illustrate the validity of the above conclusion.