The Existence Of Solutions Of Initial-boundary Problems For A Semilinear Hyperbolic Systems

In this paper, we study the existence of global solutions of Initial-boundary prob-lems for a kind of semilinear hyperbolic systems in multi-dimensions which can betransformed into a wave equation,and the purpose of it is to find common boundaryconditions which can ensure the existence of global solutions under small initial data,Infact we find a common boundary condition for this Initial-boundary problems by en-ergy method and we get the global existence of the solution by the method of prioriestimate, Then we discuss Initial-boundary problems for wave equation with dampingand get corresponding energy estimate at the basis of it,which prepare for the discussof the Initial-boundary problems of non-linear wave equation.