Riemann method for the solution of hyperbolic differential equations

In this thesis new results can be obtained by examining the given references of the classified hyperbolic partial differential equations with Cauchy and Goursat problems for the solution of differential equations and integral formulas are expressed an clear. The Cauchy and Goursat problems of existence and uniqueness of the solution of these problems equivalent Volterra system of integral equations by the method of successive approximations to the solutions has been found and proven. In this thesis, Riemann method for linear differential operator with the formula for the Green, are given here for linear differential operators are provided as required in formulas Green. Riemann method, Riemann function plays an important role in explaining. In thesis, Riemann function defined as needed to Cauchy and Goursat problems, Riemann function characteristics such symmetry and the presence of the Riemann function given method and construction method is shown in the individual cases.