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On determining sources with compact supports in a bounded plane domain for the heat equation. (English. Russian original) Zbl 1398.35295

Comput. Math. Math. Phys. 58, No. 5, 750-760 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 5, 778-804 (2018).
Summary: The inverse problem of determining the source for the heat equation in a bounded domain on the plane is studied. The trace of the solution of the direct problem on two straight line segments inside the domain is given as overdetermination (i.e., additional information on the solution of the direct problem). A Fredholm alternative theorem for this problem is proved, and sufficient conditions for its unique solvability are obtained. The inverse problem is considered in classes of smooth functions whose derivatives satisfy the Hölder condition.

MSC:

35R30 Inverse problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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