Goursat’s problem on the plane for a quasilinear hyperbolic equation

Abstract

A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator. We constructed the unique solution by the method of successive approximations and showed the necessary and sufficient smoothness and matching conditions on given functions.