On the Cauchy problem for \(p\)-evolution equations with variable coefficients: a necessary condition for Gevrey well-posedness. (English) Zbl 07901386
Summary: 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.
MSC:
| 35G10 | Initial value problems for linear higher-order PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
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