On the well-posedness of weakly hyperbolic equations with time dependent coefficients

TL;DR

This paper investigates the conditions under which weakly hyperbolic equations with time-dependent coefficients are well-posed in Gevrey spaces, considering the influence of lower order terms and multiple roots.

Contribution

It provides new well-posedness results for weakly hyperbolic equations in Gevrey and ultradistribution spaces, accounting for lower order terms and multiple roots.

Findings

Gevrey well-posedness depends on lower order terms and root multiplicity

Results extend to Gevrey Beurling ultradistributions

Conditions identified for well-posedness in variable coefficient scenarios

Abstract

In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions.