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].
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Cagnac, F. Problème de Cauchy sur un conoïde caractéristique pour des équations quasi-linéaires. Annali di Matematica pura ed applicata 129, 13–41 (1981). https://doi.org/10.1007/BF01762134
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DOI: https://doi.org/10.1007/BF01762134