The Cauchy problem for $p$-evolution equations with variable coefficients in Gevrey classes

TL;DR

This paper investigates the well-posedness of linear evolution equations of arbitrary order with variable coefficients in Gevrey spaces, under decay conditions on lower order terms, extending understanding of such PDEs.

Contribution

It establishes well-posedness results for a broad class of $p$-evolution equations with variable coefficients in Gevrey classes, considering decay conditions on coefficients.

Findings

Proves well-posedness in Gevrey spaces for variable coefficient $p$-evolution equations.

Identifies decay conditions on coefficients ensuring solution existence and uniqueness.

Extends previous results to higher-order and variable coefficient PDEs.

Abstract

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we prove a well-posedness result in Gevrey-type spaces.