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The Cauchy problem for evolution equations with non-regular coefficients. (English) Zbl 1064.35038

Summary: The authors deal with the Cauchy problem for a class of evolution operators of Schrödinger type. They find the sharp regularity of the coefficients in the time variable for the well-posedness in Gevrey classes of the homogeneous problem, then the Levi conditions in the general case are obtained.

MSC:

35G10 Initial value problems for linear higher-order PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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