Existenz- und Eindeutigkeitsbeweis zur Lösung des Goursat-Problems für quasilineare hyperbolische Systeme erster Ordnung mittels Differenzenverfahren. (Proof of existence and uniqueness of the solution of the Goursat problem for quasilinear hyperbolic systems of first order by difference methods) (Q1081026)

This paper continues the author's investigation [ibid. 4, 65-83 (1985; Zbl 0565.35070)] 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 he obtains ''continuable initial conditions''. Moreover, using an a priori estimate for a certain linear problem he can show the uniqueness of the solution of the original problem and its continuous dependence on parameters.