Smooth Approxiation Of Two Classes Of Stochastic Partial Differential Equations

In this thesis,we mainly investigate the smooth approximation of manifolds for two classes of stochastic partial differential equations:one is the smooth approximation of the center manifold of the stochastic parabolic equation with multiplicative noise,the other is the smooth approximation of the inertial manifold of the stochastic wave equation with additive noise.For the stochastic parabolic equation with multiplicative noise,since the Wiener process(?)is continuous but not smooth everywhere,we use the stochastic process(?),which is continuous everywhere and smooth everywhere,to approximate it.We first transform the original system into a random system,and then drive the existence of the center manifold of the original stochastic system and approximate system.Using the properties of the exponential trichotomy,we show that the center manifold of the original stochastic system converges to that of the approximate system.For the stochastic wave equation with additive noise,using the same argument,after establish the existence of inertial manifolds of the original stochastic system and the approximate system,we verify that the inertial manifold of the original stochastic system converges to that of the approximate system.