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Cauchy problem for some semilinear evolution equations. (English) Zbl 1049.35075
The paper deals with semilinear evolution equations involving hyperbolic and Schrödinger equations as well. The maximum order is specified of the derivatives in the nonlinear part which yields well-posedness of the Cauchy problem in Sobolev spaces of the evolution equations. An example is given to show that the well-posedness may fail if that order is exceeded.

35G10 Initial value problems for linear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35G05 Linear higher-order PDEs
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