On the $C^∞$-well-posedness of Goursat Problems

Many authors have investigated about null-solutions of characteristic Cauchy problems. When the coefficients are real-analytic, many systematic results have been obtained. When the coefficients are only C°°, however, few results are known. In this paper, as one of the cases when we can get well-parametrized null-solutions , we consider Goursat problems on Rn+l(n^l). To give more explanation, we introduce some notations as follows;