Initial-Boundary Value Problems For A High Order Hyperbolic Equation Wity Nonlocal Boundary Conditions

The present paper is devoted to the investigation of a nonlinear Hyperbolic Equation with nonlocal boundary conditions by means of the Galerkin method.Existence,uniqueness and continuous dependence upon data of a weak solution are proved,and finally get the exponential decay of energy of the system. The full text structure is as follows:The first chapter briefly introduces the background of the research,the main work in this paper, and at the same time the main results are obtained.The second chapter introduces some basic knowledge used in this paper, including the basic space as well as their relationship, lemma and some commonly used inequality.Third chapter the first sectionis ia devoted to the initial-boundary value problem of a nonlinear Telegraph Equation with nonlocal boundary conditions by means of the Galerkin method,the existence and uniqueness of weak solution and continuous dependence on initial value,the exponential decay of energy of the system are proved.Four chapter it is generalized to the initial-boundary value problem of higher order hyperbolic equation with nonlocal boundary conditions in a specific space,the existence and uniqueness of weak solution and continuous dependence on initial value,the exponential decay of energy of the system are proved.Five chapter take its applications into nonlinear beam equation, parabolic equation, Sine-Gordon equation and obtain some conclusion.