Inverse problems with pointwise overdetermination for some quasilinear parabolic systems

S. G. Pyatkov ; V. V. Rotko

Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 178-204.

Résumé

In the article, we examine well-posedness questions in the Sobolev spaces of the inverse source problem in the case of a quasilinear parabolic system of the second order. The main part of the operator is linear. The overdetermination conditions are values of a solution at some collection of interior points. It is demonstrated that, in the case of at most linear growth of the nonlinearity, there exists a unique global (in time) solution and the problem is well-posed in the Sobolev classes. The conditions on the data are minimal and the results are sharp.

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