Geodesic
Inverse problem for semilinear ultraparabolic equation of higher order
Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 395-404

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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.
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.
DOI : 10.21136/MB.2015.144458
Classification : 35K70, 35R30
Keywords: ultraparabolic equation; mixed problem; inverse problem; weak solution 
Protsakh, Nataliya. Inverse problem for semilinear ultraparabolic equation of higher order. Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 395-404. doi: 10.21136/MB.2015.144458
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