Jce. Silva et C. Leal, THE GENERALIZED GOURSAT-DARBOUX PROBLEM FOR A 3RD-ORDER OPERATOR, Proceedings of the American Mathematical Society, 125(2), 1997, pp. 471-475
It is proved that if a generalized Goursat-Darboux problem is C-infini
ty-well posed then the operator cannot contain derivatives with respec
t to one of the variables.