in two independent variables from its given values on two smooth monotone curves and , issuing from the same point and located in the characteristic angle with apex at . In particular, and may partly or wholly coincide with the sides of this angle.

This problem has been studied for equations of the form . Goursat's problem is sometimes referred to as the Darboux problem. The Goursat problem for hyperbolic equations of order two in several independent variables is often understood to be the characteristic problem, viz. to find its