Geodesic
Identification of thermophysical parameters in mathematical models of heat and mass transfer
Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 52-66.

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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. 
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     author = {S. G. Pyatkov},
     title = {Identification of thermophysical parameters in mathematical models of heat and mass transfer},
     journal = {Journal of computational and engineering mathematics},
     pages = {52--66},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2022_9_2_a4/}
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S. G. Pyatkov. Identification of thermophysical parameters in mathematical models of heat and mass transfer. Journal of computational and engineering mathematics, Tome 9 (2022) no. 2, pp. 52-66. http://geodesic.mathdoc.fr/item/JCEM_2022_9_2_a4/