# Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane

## TL;DR

This paper proves well-posedness of the Cauchy problem for effectively hyperbolic operators with triple characteristics on the initial plane, removing previous restrictive conditions and extending prior results.

## Contribution

It establishes well-posedness without assuming the previously required condition (E), advancing the understanding of hyperbolic operators with triple characteristics.

## Key findings

- Well-posedness of the Cauchy problem for operators with triple characteristics.
- Removal of the condition (E) from previous assumptions.
- Extension of results to more general hyperbolic operators.

## Abstract

We study effectively hyperbolic operators $P$ with triple characteristics points lying on $t= 0$. Under some conditions on the principal symbol of $P$ one proves that the Cauchy problem for $P$ in $[0, T] \times U$ is well posed for every choice of lower order terms. Our results improves those in [11] since we don't assume the condition (E) of [11] satisfied.