Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
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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: firstname.lastname@example.org
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.
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