The Given Problem Of The Linear Hyperbolic Equations With Two-independent Variables

This paper is concerned with the given problem of the general linear hyperbolic equations with two-independent variables. The solution to the Goursat problem of the equations is obtained by means of the classical characteristic method and the successive approximation method. The existence and uniqueness of the classical solution is analysed and then the continus dependence on the boundary conditions of the problem is discussed. We also prove that the generalized Cauchy problem of the equations can be converted into the conresponding Cauchy problem, then we obtain the solution of them. At last, the giving problem of the general angular-domainal boundary value problem is discussed.This paper consists of three Chapters.1. In Chapter one, the definite problem of the hyperbolic equations is given.2. In Chapter two, the solution to the Goursat problem of the equations is obtained and then the existence, uniqueness and stability is discussed.3. An idea of solving the generalized Cauchy problem and angle-domainal boundary value problem is presented in Chapter three.