Well-postdness And Dynamics Of Several Kinds Of Stochastic Partiax Differential Equations

As we know,the complex systems corresponding to natural phenomena often have some random or uncertain factors.With the development of physics,chemistry,biology,it was found that when the nonlinear wave in the random medium and the white noise,there will be some new characteristics.A number of facts show that the deterministic equations under the disturbance of random noise will produce new phenomenon,which has caused the wide attention of scholars.This paper is devoted to the well-posedness and dynamics of several kinds of stochastic partial differential equations.We mainly investigate the stochastic degenerate parabolic e-quations,stochastic p-Laplace equations and non-autonomous retarded degenerate parabolic equation,respectively.First,the Wong-ZaKai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered.We first establish the existence and uniqueness of tempered pullback attractors for the Wong-ZaKai approximations of s-tochastic degenerate parabolic equations.We then prove that the attractors of Wong-ZaKai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.Then,we investigate the Wong-ZaKai approximations for stochastic p-Laplace equa-tions.We prove the existence and uniqueness of tempered pullback attractors for the Wong-ZaKai approximations of stochastic p-Laplace equations.We then prove that the attractors of Wong-ZaKai approximations converge to the attractor of stochastic p-Laplace equations driven by multiplicative white noise.At last,we are devoted to a non-autonomous retarded degenerate parabolic equation.We first show the existence and uniqueness of a weak solution for the equation by using the standard Galerkin method.Then we establish the existence of pullback attractors for the equation by proving the existence of compact pullback absorbing sets and the pullback asymptotic compactness.