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A. I. Prilepko, D. S. Tkachenko

Inverse problem for a parabolic equation with integral overdetermination

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.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 11, 06/2003
Pages: 191 - 218

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