Periodic Solutions Of Several Types Of Nonlinear Parabolic Equations(Systems)

In this paper, we study the periodic problem of nonlinear parabolic equations with Neumann boundary conditions. This article is mainly composed of the following four parts.In Chapter1, we mainly introduce the background and preliminaries of the nonlinear parabolic equation.In Chapter2, we study the periodic boundary value problem of a p-Laplacian equa-tion with nonlocal terms and Neumann boundary value conditions. Since the equation is degenerate, we first establish the regular problem. By Moser iteration technique, we establish a priori upper bound of the solution by Moser iteration technique. Then by the method of contradiction, we obtain a priori lower bound of the solution. Then by the theory of Leray-Schauder degree, we establish the existence of the nontrivial nonnegative periodic solution of the regular problem. At last, we obtain the existence of the nontrivial nonnegative periodic solution of the original problem by a limit process.In Chapter3, on the assumption that the nonlocal items meet certain bound restric-tions, we establish the existence of the nontrivial nonnegative periodic solution of the quasilinear parabolic equations with nonlocal terms and Neumann boundary value condi-tions.In Chapter4, we study the two-species degenerate Lotka-Volterra system. This sys-tem is a weak coupled degenerate parabolic system and is used to describe competition of two groups. We first establish the existence of the nonnegative solution of the initial boundary value problem by the method of parabolic regularization. Then by the theory of Leray-Schauder degree, we obtain the existence of the nontrivial nonnegative periodic solution.