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. 
@article{MZM_2003_73_2_a5,
     author = {V. L. Kamynin},
     title = {On the {Unique} {Solvability} of an {Inverse} {Problem} for {Parabolic} {Equations} under a {Final} {Overdetermination} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {217--227},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/}
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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/