Existenz- und Eindeutigkeitsbeweis zur Lösung des Goursat-Problems für quasilineare hyperbolische Systeme erster Ordnung mittels Differenzenverfahren

Abstract

This paper continues the author’s investigations [8] on the mixed problem for quasi-linear hyperbolic systems of the first order. For a special Goursat problem to which the general problem was reduced the solvability in the class of Lipschitz continuous functions is proved by means of a suitable difference method. Thereby we obain "continuable initial conditions". Moreover, using an a priori estimate for a certain linear problem we can show the uniqueness of the solution of the original problem and its continuous dependence on parameters.