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Inverse problem for semilinear ultraparabolic equation of higher order. (English) Zbl 1363.35210
Summary: We study the existence and the uniqueness of the weak solution of an inverse problem for a semilinear higher order ultraparabolic equation with Lipschitz nonlinearity. The main aim is to determine the weak solution of the equation and some functions that depend on the time variable, appearing on the right-hand side of the equation. The overdetermination conditions introduced are of integral type. In order to prove the solvability of this problem in Sobolev spaces we use the Galerkin method and the method of successive approximations.

MSC:
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
35R30 Inverse problems for PDEs
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