Abstract:
We examine well-posedness questions in the Sobolev spaces of inverse problems of recovering coefficients depending on time in a parabolic system. The overdetermination conditions are values of a solution at some collection of points lying inside the domain and on its boundary. The conditions obtained ensure existence and uniqueness of solutions to these problems in the Sobolev classes.
Received: 10.03.2021 Received in revised form: 05.04.2021 Accepted: 20.05.2021
Bibliographic databases:
Document Type:
Article
UDC:517.95
Language: English
Citation:
Sergey G. Pyatkov, Vladislav A. Baranchuk, “On some inverse parabolic problems with pointwise overdetermination”, J. Sib. Fed. Univ. Math. Phys., 14:4 (2021), 463–474
\Bibitem{PyaBar21}
\by Sergey~G.~Pyatkov, Vladislav~A.~Baranchuk
\paper On some inverse parabolic problems with pointwise overdetermination
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 4
\pages 463--474
\mathnet{http://mi.mathnet.ru/jsfu931}
\crossref{https://doi.org/10.17516/1997-1397-2021-14-4-463-474}
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https://www.mathnet.ru/eng/jsfu/v14/i4/p463
This publication is cited in the following 4 articles:
Sergey Pyatkov, Alexey Potapkov, Kudratillo Fayazov, “Inverse Problems of Recovering a Source in a Stratified Medium”, J Math Sci, 281:6 (2024), 925
A. I. Kozhanov, T. N. Shipina, “Linear inverse problems for the heat equation and non-local boundary value problems with generalized Samarskii–Ionkin condition”, Bol. Soc. Mat. Mex., 29:3 (2023)
A. I. Kozhanov, T. N. Shipina, “Nonlinear Inverse Problems for Parabolic Equations with Time–Dependent Coefficients. Reduction to Nonlocal Problems with Samarskii–Ionkin Type Conditions”, J Math Sci, 274:4 (2023), 523
S. G. Pyatkov, “On inverse problems with pointwise overdetermination for mathematical models of heat and mass transfer”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:3 (2022), 34–50
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