On The Existence And Uniqueness Of Solution For Some Boundary Value Problems Of PDEs

Boundary value problems of partial differential equations have diverse sources and applications in pratice and theory respectively. This thesis focuses on existence and uniqueness of solution for some boundary value problems of partial differential equations. There are three chapters. In first chapter, we mainly present research histories and situations of studys with respect to existence of solution for Boundary value problems of PDEs. We discuss the existence and uniqueness of solution for a class of systems of hyperbolic partial differential equations . In the last chapter, we consider the existence and uniqueness of solution for boundary value problems of system of partial differential equations with x-dependent coefficients. In the study of the two classes of partial differential equations, we make use of the global inverse theorem and Garlerkin's methods.