On the Levi condition for Goursat problem

Abstract

We consider the Goursat problem in the class of $C^{\infty}$-function. First, we consider the case of constant coefficients. We give a Levi’s condition which is analogous to A. Lax’s theorem [2] for the hyperbolic operator. Next, we consider the case of variable coefficients. In this case we give a sufficient condition for wellposedness of Goursat problem.