The Cauchy problem for properly hyperbolic equations in one space variable.

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 τ j verify an inequality like τ j 2 (x) + τ k 2 (x) ≤ M (τ j (x) − τ k (x)) 2. We prove that the Cauchy problem is well-posed in ∞ if the operators with frozen coefficients are uniformly hyperbolic in the sense of Gårding. [ABSTRACT FROM AUTHOR]