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.
On the Cauchy problem for p-evolution equations with variable coefficients: A necessary condition for Gevrey well-posedness
Marco Cappiello
2024-01-01
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.
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