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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 11, Issue 2 (Jun 2003)


Inverse problem for a parabolic equation with integral overdetermination

A. I. Prilepko
  • Mech.-Math. Faculty, Moscow State University, GSP-2, Leninskie Gory, 119992, Moscow, Russia
/ D. S. Tkachenko
  • Moscow Engineering-Physics Institute, Kashirskoe Shosse, 31, 115409, Moscow, Russia. E-mail:

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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Published in Print: 2003-06-01

Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939403766493546. Export Citation

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