Geodesic
On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 217-227.

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We consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition. We obtain two types of conditions that are sufficient for the local solvability of the inverse problem and also prove the so-called Fredholm solvability of the inverse problem under study. 
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V. L. Kamynin. On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 217-227. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/

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