On the Cauchy problem for $p$-evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness

Abstract

In this paper we consider a class of $p$-evolution equations of arbitrary order with variable coefficients depending on time and space variables $(t,x)$. We prove necessary conditions on the decay rates of the coefficients for the well-posedness of the related Cauchy problem in Gevrey spaces.

20 pages