Geodesic
On an Inverse Problem for a Parabolic Equation
Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 729-743.

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In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in $u$ in which the coefficients of $u_t$ and $u$ depend on $u_(x,t)$ , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established. 
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D. S. Tkachenko. On an Inverse Problem for a Parabolic Equation. Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 729-743. http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a9/

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