Initial-boundary Value Problems For A Coupled Nonlinear Partial Differential Equaltions With Memory Terms

In this paper,we studied an initial-boundary value problem for a coupled nonlinear par?tial differential equations with memory terms.By employing the Faedo-Galerkin method and combining with the prior integral estimation,the coupled terms and nonlinear terms are solved effectively.Existence,uniqueness and continuous dependence upon initial data of the weak solution are proved.In the end,existence of the strong solution and classical solution of the equations are proved by strengthening the assumptions.The paper is arranged as follows:The first chapter,the development and research at home and abroad relevant with the coupled nonlinear partial differential equations and the main work of this paper are intro-duced.The second chapter,some basic spaces,lemmas are given,and some symbols are ex-plained properly.The third chapter,existence,uniqueness and continuous dependence upon initial data of the weak solution of the coupled nonlinear partial differential equations with memory terms are proved.The four chapter,existence of the strong solution of the equations is obtained with the condition of boundary unchanged and improved smoothness of initial data.The five chapter,existence of the classical solution of the equations is obtained under the assumed conditions that are changed properly and improved smoothness of initial data.The six chapter,the main contents of this paper are summarized,and the research orien-tations in the future is introduced.