Abstract:
We examine an inverse problem of determining the right-hand side (source function) in a parabolic equation from integral overdetermination data. By a solution to a parabolic equation we mean a weak solution, and the right-hand side in this equation can be a distribution of a certain class. Under some conditions on the data of the problem, we demonstrate that this inverse problem is well-posed and, in particular, stability estimates hold.
Keywords:
inverse problem, second-order parabolic equation, boundary value problem, integral overdetermination condition, weak solution.
Citation:
S. G. Pyatkov, M. V. Uvarova, “On determining the source function in heat and mass transfer problems under integral overdetermination conditions”, Sib. Zh. Ind. Mat., 19:4 (2016), 93–100; J. Appl. Industr. Math., 10:4 (2016), 549–555
\Bibitem{PyaUva16}
\by S.~G.~Pyatkov, M.~V.~Uvarova
\paper On determining the source function in heat and mass transfer problems under integral overdetermination conditions
\jour Sib. Zh. Ind. Mat.
\yr 2016
\vol 19
\issue 4
\pages 93--100
\mathnet{http://mi.mathnet.ru/sjim942}
\crossref{https://doi.org/10.17377/sibjim.2016.19.410}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588967}
\elib{https://elibrary.ru/item.asp?id=27208361}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 4
\pages 549--555
\crossref{https://doi.org/10.1134/S1990478916040116}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84996559100}
Linking options:
https://www.mathnet.ru/eng/sjim942
https://www.mathnet.ru/eng/sjim/v19/i4/p93
This publication is cited in the following 4 articles:
K. B. Sabitov, “Inverse problems of finding a source in the heat equation from a nonlocal observation”, J. Appl. Industr. Math., 18:3 (2024), 536–547
S. G. Pyatkov, “On evolutionary inverse problems for mathematical models of heat and mass transfer”, Bull. South Ural State U. Ser.-Math Model Program Comput., 14:1 (2021), 5–25
A. Yu. Chebotarev, “Inverse problem for equations of complex heat transfer with Fresnel matching conditions”, Comput. Math. Math. Phys., 61:2 (2021), 288–296
G. V. Grenkin, A. Yu. Chebotarev, “Inverse problem for equations of complex heat transfer”, Comput. Math. Math. Phys., 59:8 (2019), 1361–1371
Citation in format AMSBIB
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