Über das Goursat-Problem für quasilineare hyperbolische Systeme partieller Differentialgleichungen erster Ordnung mit zwei unabhängigen Variablen

Abstract

This paper deals with the mixed problem for quasi-linear hyperbolic system of the first order in two variables. At first we investigate how many boundary conditions may be set and what the necessary conditions of solvability (compatibility conditions) are. In preparation for the existence proof in the function class $C^{k,1}$ we reduce the original problem to a special Goursat problem. Then the corresponding system (prolonged system) has diagonal form and it is sufficient to prove the existence of Lipschitz continuous solutions for this problem.