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. 
@article{MZM_2004_75_5_a9,
     author = {D. S. Tkachenko},
     title = {On an {Inverse} {Problem} for a {Parabolic} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {729--743},
     publisher = {mathdoc},
     volume = {75},
     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a9/}
}
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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/