Abstract:
Under consideration are mathematical models of heat and mass transfer. We consider inverse problems of recovering coefficients in the main part of a parabolic equation occurring simultaneously in a Robin-type boundary condition. The overdetermination conditions are values of a solution at some collection of points lying inside the domain. In particular, in the class of these inverse problems the classical problems of recovering the thermal conductivity tensor are included. The main attention is paid to existence, uniqueness, and stability estimates for solutions to inverse problems of this type. The problem is reduced to an operator equation which is studied with the use of the fixed point theorem and a priori estimates. The method of the proof is constructive and it can be used in developing new numerical algorithms for solving the problem.
Keywords:
inverse problem, heat and mass transfer, heat conductivity, parabolic equation.
This research was funded by the Russian Science Foundation and the government of Khanty-Mansiysk autonomous okrug-Yugra (Grant 22-11-20031).
Received: 07.05.2022
Document Type:
Article
UDC:517.956
Language: English
Citation:
S. G. Pyatkov, “Identification of thermophysical parameters in mathematical models of heat and mass transfer”, J. Comp. Eng. Math., 9:2 (2022), 52–66
\Bibitem{Pya22}
\by S.~G.~Pyatkov
\paper Identification of thermophysical parameters in mathematical models of heat and mass transfer
\jour J. Comp. Eng. Math.
\yr 2022
\vol 9
\issue 2
\pages 52--66
\mathnet{http://mi.mathnet.ru/jcem215}
\crossref{https://doi.org/10.14529/jcem220205}
Linking options:
https://www.mathnet.ru/eng/jcem215
https://www.mathnet.ru/eng/jcem/v9/i2/p52
This publication is cited in the following 3 articles:
Sergey Pyatkov, Oleg Soldatov, “Inverse Problems of Recovering Lower-Order Coefficients from Boundary Integral Data”, Axioms, 14:2 (2025), 116
S. Pyatkov, T. Pronkina, “Coefficient Inverse Problems of Identification of Thermophysical Parameters From Boundary Integral Data”, J Math Sci, 284:2 (2024), 241
S. G. Pyatkov, O. A. Soldatov, “On some classes of inverse parabolic problems of recovering the thermophysical parameters”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:3 (2023), 23–33