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

https://doi.org/10.29235/1561-8323-2022-66-4-391-396

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.

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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)