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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 9, Pages 1537–1552
DOI: https://doi.org/10.31857/S0044466923090053 (Mi zvmmf11619) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical physics

Inverse problems for the diffusion-drift model of charging of an inhomogeneous polar dielectric

R. V. Brizitskiia, N. N. Maksimovab, A. G. Maslovskayab

a Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia
b Amur State University, 675000, Blagoveshchensk, Amur oblast, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923090053
Abstract: The problems of reconstructing the unknown parameters of the model of electron-induced charging of an inhomogeneous polar dielectric from additional information about the volume charge density distribution and the electric field strength are studied. Within the optimization approach, these inverse problems are reduced to control problems and their solvability is proved. For extremum problems, optimality systems are derived and, based on their analysis, local uniqueness of the solution of one of the considered problems is proved. Taking into account the introduced characteristic of the inhomogeneity of the dielectric, auxiliary results on the solvability and properties of solutions of the boundary value problem, obtained earlier for the model of charging of a homogeneous dielectric, are corrected.
Key words: electron drift-diffusion model, model of charging of an inhomogeneous polar dielectric, global solvability, local uniqueness, maximum principle, inverse problem, control problem, optimality system.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-01290-23-00
122082400001-8
075-02-2023-946
This work was carried as part of the government order no. 075-01290-23-00 to the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, and was supported by the Ministry of Science and Higher Education of the Russian Federation (project nos. 122082400001-8 and 075-02-2023-946).
Received: 12.02.2023
Revised: 12.02.2023
Accepted: 29.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 9, Pages 1685–1699
DOI: https://doi.org/10.1134/S0965542523090051
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: R. V. Brizitskii, N. N. Maksimova, A. G. Maslovskaya, “Inverse problems for the diffusion-drift model of charging of an inhomogeneous polar dielectric”, Zh. Vychisl. Mat. Mat. Fiz., 63:9 (2023), 1537–1552; Comput. Math. Math. Phys., 63:9 (2023), 1685–1699
Citation in format AMSBIB
\Bibitem{BriMakMas23}
\by R.~V.~Brizitskii, N.~N.~Maksimova, A.~G.~Maslovskaya
\paper Inverse problems for the diffusion-drift model of charging of an inhomogeneous polar dielectric
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 9
\pages 1537--1552
\mathnet{http://mi.mathnet.ru/zvmmf11619}
\crossref{https://doi.org/10.31857/S0044466923090053}
\elib{https://elibrary.ru/item.asp?id=54313687}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 9
\pages 1685--1699
\crossref{https://doi.org/10.1134/S0965542523090051}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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