Abstract:
We study the Sobolev space well-posedness of inverse problems of determining the heat transfer coefficient contained in a Robin-type boundary condition for the convection-diffusion equations. We prove an existence and uniqueness theorem for the solutions.
Keywords:
inverse problem, heat transfer coefficient, parabolic equation, heat and mass transfer, diffusion.
This work was supported by the Russian Science Foundation
and the Government of the Khanty-Mansiysk Autonomous Okrug-YUGRA
under grant no. 22-11-20031.
Citation:
S. G. Pyatkov, V. A. Baranchuk, “Determination of the Heat Transfer Coefficient in Mathematical Models of Heat and Mass Transfer”, Mat. Zametki, 113:1 (2023), 90–108; Math. Notes, 113:1 (2023), 93–108
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\by S.~G.~Pyatkov, V.~A.~Baranchuk
\paper Determination of the Heat Transfer Coefficient in Mathematical Models of Heat and Mass Transfer
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 1
\pages 90--108
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\crossref{https://doi.org/10.4213/mzm13573}
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\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 1
\pages 93--108
\crossref{https://doi.org/10.1134/S0001434623010108}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149995814}
Linking options:
https://www.mathnet.ru/eng/mzm13573
https://doi.org/10.4213/mzm13573
https://www.mathnet.ru/eng/mzm/v113/i1/p90
This publication is cited in the following 9 articles:
S. G. Pyatkov, O. A. Soldatov, “Identification of the Heat Transfer Coefficient from Boundary Integral Data”, Sib Math J, 65:4 (2024), 824
S. G. Pyatkov, O. A. Soldatov, “Identifikatsiya koeffitsienta teploperedachi po granichnym integralnym dannym”, Sib. matem. zhurn., 65:4 (2024), 709–726
E. I. Safonov, S. G. Pyatkov, “The flux recovering at the ecosystem-atmosphere boundary by inverse modelling”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 17:3 (2024), 29–45
A. Yu. Chebotarev, “Inverse Problem for Quasi-Stationary Complex Heat Transfer Equations with Fresnel Matching Conditions”, Comput. Math. and Math. Phys., 64:10 (2024), 2269
A. Yu. Chebotarev, “Obratnaya zadacha s integralnym pereopredeleniem dlya polulineinogo parabolicheskogo uravneniya”, Dalnevost. matem. zhurn., 24:2 (2024), 280–285
S. G. Pyatkov, V. A. Belonogov, “Opredelenie koeffitsienta teploobmena v zadachakh sopryazheniya s usloviyami neidealnogo kontakta”, Chelyab. fiz.-matem. zhurn., 8:3 (2023), 331–350
S. N. Shergin, S. G. Pyatkov, “Recovering of the heat transfer coefficient from the temperature measurements”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:3 (2023), 51–64
Sergey Pyatkov, Alexey Potapkov, “The well-posed identification of the interface heat transfer coefficient using an inverse heat conduction model”, Mathematics, 11:23 (2023), 4739
Sergey Pyatkov, Oleg Soldatov, Kudratillo Fayazov, “Inverse problems of recovering the heat transfer coefficient with integral data”, J Math Sci, 274:2 (2023), 255
Citation in format AMSBIB
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