Sur les équations hyperboliques à coefficients analytiques par rapport aux variables spaciales

Abstract

J.-M. Bony and P. Schapira [1] showed that the hyperbolicity asserted the global existence of solutions of the Cauchy problem in the space of analytic functions. In this article we show that this claim is also valid for the equations with continuous coefficients which are analytic with respect to the space variables. We follow the reasoning of J.-M. Bony and P. Schapira except the following point: we use the analyticity of solutions of the elliptic eqations in the place of the Homgren transformation.