Problème de Cauchy sur un conoïde caractéristique pour des équations quasi-linéaires

Summary Cauchy problem for system of quasilinear differential equations of order two on a characteristic conoid is solved. It is proved that, given a conoid with the values of the unknown functions on it such that it is a characteristic conoid, there is a unique solution, which is smooth at the apex of the conoid. This result is obtained under smoothness conditions on the data and some supplementary conditions on the data at the apex of the conoid, and by use of Leray's theory 6].