Une condition suffisante pour que le probl\`eme de Cauchy soit bien pos\'e

TL;DR

This paper establishes an energy estimate for the Cauchy problem involving hyperbolic equations with double characteristics, addressing both effectively and non-effectively hyperbolic points.

Contribution

It provides a new energy estimate that ensures well-posedness for hyperbolic equations with complex characteristic structures.

Findings

Energy estimate valid for equations with double characteristics

Addresses both effectively and non-effectively hyperbolic points

Contributes to understanding well-posedness of such problems

Abstract

We prove here an energy estimate for the Cauchy problem for hyperbolic equations with double characteristics which contains both effectively hyperbolic and non effectively hyperbolic points.