The Cauchy problem for properly hyperbolic equations in one space variable

Abstract

In this paper, we consider the Cauchy problem for higher-order weakly hyperbolic equations assuming that the principal symbol depends only on one space variable and the characteristic roots [Formula: see text] verify an inequality like [Formula: see text] We prove that the Cauchy problem is well-posed in [Formula: see text] if the operators with frozen coefficients are uniformly hyperbolic in the sense of Gårding.