Darboux and Goursat type problems in the trihedral angle for hyperbolic type equations of third order (Q1378838)

The author considers in \(\mathbb{R}^3\) the third order partial differential equation \(D^3_{x_1 x_2x_3} u=f\), where \(f\) is a given function. Darboux and Goursat problems are studied in a trihedral angle \(D\). After a change of variables, mapping \(D\) into the domain \(\{y_1>0, y_2>0, y_3>0\}\), solutions are investigated by direct methods.