Abstract
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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Tkachenko, D.S. On an Inverse Problem for a Parabolic Equation. Mathematical Notes 75, 676–689 (2004). https://doi.org/10.1023/B:MATN.0000030976.63035.e1
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DOI: https://doi.org/10.1023/B:MATN.0000030976.63035.e1