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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2021, Volume 14, Issue 1, Pages 5–25 (Mi vyuru578)  

Review Articles

On evolutionary inverse problems for mathematical models of heat and mass transfer

S. G. Pyatkov

Yugra State University, Khanty-Mansiisk, Russian Federation

Abstract: This article is a survey. The results on well-posedness of inverse problems for mathematical models of heat and mass transfer are presented. The unknowns are the coefficients of a system or the right-hand side (the source function). The overdetermination conditions are values of a solution of some manifolds or integrals of a solution with weight over the spatial domain. Two classes of mathematical models are considered. The former includes the Navier–Stokes system, the parabolic equations for the temperature of a fluid, and the parabolic system for concentrations of admixtures. The right-hand side of the system for concentrations is unknown and characterizes the volumetric density of sources of admixtures in a fluid. The unknown functions depend on time and some part of spacial variables and occur in the right-hand side of the parabolic system for concentrations. The latter class is just a parabolic system of equations, where the unknowns occur in the right-hand side and the system as coefficients. The well-posedness questions for these problems are examined, in particular, existence and uniqueness theorems as well as stability estimates for solutions are exposed.

Keywords: inverse problem, heat and mass transfer, filtration, diffusion, well-posedness.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00620_a
The author was supported by the Russian foundation for basic research (Grant 18-01-00620a).


DOI: https://doi.org/10.14529/mmp210101

Full text: PDF file (296 kB)
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UDC: 517.956
MSC: 35R30, 35Q35, 65M60, 65M32
Received: 19.08.2020
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Citation: S. G. Pyatkov, “On evolutionary inverse problems for mathematical models of heat and mass transfer”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:1 (2021), 5–25

Citation in format AMSBIB
\Bibitem{Pya21}
\by S.~G.~Pyatkov
\paper On evolutionary inverse problems for mathematical models of heat and mass transfer
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2021
\vol 14
\issue 1
\pages 5--25
\mathnet{http://mi.mathnet.ru/vyuru578}
\crossref{https://doi.org/10.14529/mmp210101}


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