In the present work, we examine an inverse problem of recovery the right-hand side (of a special form) of a parabolic equation with variable coefficients. As overdetermination, a time integral of solution is specified. Such a problem is proved to possess the Fredholm property; also proved is the existence and uniqueness of its solution provided that the operator coefficients at higher-order derivatives with respect to spatial variables are stationary. Stability estimates are given. Some easily verifiable sufficient conditions for correct solvability of the inverse problem "on the whole" are found.
Editor-in-Chief: Kabanikhin, Sergey I.
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Inverse problem for a parabolic equation with integral overdetermination
∗Mech.-Math. Faculty, Moscow State University, GSP-2, Leninskie Gory, 119992, Moscow, Russia
†Moscow Engineering-Physics Institute, Kashirskoe Shosse, 31, 115409, Moscow, Russia. E-mail: sdtk@mail1.lebedev.ru
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 11, Issue 2, Pages 191–218, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939403766493546,
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