On weakly hyperbolic equations with analytic principal part

TL;DR

This paper extends well-posedness results for weakly hyperbolic equations with analytic coefficients by incorporating low order terms through a novel reduction method, establishing Levi conditions for continued $C^{ abla}^ ext{infty}$ well-posedness.

Contribution

It introduces a new reduction approach to include low order terms in well-posedness analysis of weakly hyperbolic equations with analytic principal parts.

Findings

Established Levi conditions ensuring $C^{ abla}^ ext{infty}$ well-posedness with low order terms

Extended previous results to broader class of weakly hyperbolic equations

Provided a new methodology for reduction to systems in this context

Abstract

In this paper we show how to include low order terms in the $C^{\infty}$ well-posedness results for weakly hyperbolic equations with analytic time-dependent coefficients. This is achieved by doing a different reduction to a system from the previously used one. We find the Levi conditions such that the $C^{\infty}$ well-posedness continues to hold.