Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 193, Pages 122–129
DOI: https://doi.org/10.36535/0233-6723-2021-193-122-129 (Mi into806) 		 
On the well-posedness of mathematical models of diffusion due to a sharply focused electron probe in a homogeneous semiconductor material

M. A. Stepovicha, D. V. Turtinb, E. V. Sereginac

a Tsiolkovsky Kaluga State University
b Plekhanov Russian State University of Economics, Moscow
c Kaluga Branch of Bauman Moscow State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2021-193-122-129
Abstract: In this paper, we compare qualitative properties of two- and three-dimensional mathematical models of the diffusion of particles (nonequilibrium minority charge carriers, excitons) generated by a sharply focused electron probe in a homogeneous semiconductor material. We show that the mathematical models considered are well posed and can be used for estimating electrophysical parameters of homogeneous semiconductor targets based on the results of experimental measurements.
Keywords: mathematical model, differential equation, partial derivative, Cauchy problem, electron probe, semiconductor, well-posedness, uniqueness, continuous dependence on data, identification.
Funding agency Grant number
Russian Foundation for Basic Research 19-03-00271
18-41-400001
The work was supported by the Russian Foundation for Basic Research and the Government of the Kaluga Region (project Nos. 19-03-00271 and 18-41-400001).
Document Type: Article
UDC: 517.95, 517.958
MSC: 35G16, 35A02, 78A35
Language: Russian
Citation: M. A. Stepovich, D. V. Turtin, E. V. Seregina, “On the well-posedness of mathematical models of diffusion due to a sharply focused electron probe in a homogeneous semiconductor material”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 122–129
Citation in format AMSBIB
\Bibitem{SteTurSer21}
\by M.~A.~Stepovich, D.~V.~Turtin, E.~V.~Seregina
\paper On the well-posedness of mathematical models of diffusion due to a sharply focused electron probe in a homogeneous semiconductor material
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 193
\pages 122--129
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into806}
\crossref{https://doi.org/10.36535/0233-6723-2021-193-122-129}
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