Abstract:
The article is devoted to the research of the Cauchy problem for a
mathematical model of the distribution of potentials in a crystalline semiconductor. By a semiconductor we mean a substance with finite electrical conductivity, which rapidly increases with increase in the temperature. The mathematical model of the distribution of potentials is based on the semi-linear Sobolev type equation supplemented by the Dirichlet and Cauchy conditions.
We use the phase space method to construct sufficient conditions for the existence of the solution to the model under study. The conditions for the continuability of the solution are given.
Keywords:
Sobolev type equations, mathematical model of distribution of potentials in crystalline semiconductor, phase space method, quasi-stationary trajectories.
Citation:
N. A. Manakova, K. V. Vasiuchkova, “Research of one mathematical model of the distribution of potentials in a crystalline semiconductor”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:2 (2019), 150–157
\Bibitem{ManVas19}
\by N.~A.~Manakova, K.~V.~Vasiuchkova
\paper Research of one mathematical model of the distribution of potentials in a crystalline semiconductor
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2019
\vol 12
\issue 2
\pages 150--157
\mathnet{http://mi.mathnet.ru/vyuru496}
\crossref{https://doi.org/10.14529/mmp190213}
\elib{https://elibrary.ru/item.asp?id=38225245}
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This publication is cited in the following 5 articles:
K. V. Perevozchikova, “The analysis and processing of information for one stochastic system of the Sobolev type”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:2 (2023), 14–20
K. V. Perevozhikova, N. A. Manakova, “Research of the optimal control problem for one mathematical model of the Sobolev type”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:4 (2021), 36–45
K. V. Perevozhikova, N. A. Manakova, A. S. Kuptsova, “Issledovanie razlichnykh tipov zadach upravleniya dlya odnoi modeli nelineinoi filtratsii”, J. Comp. Eng. Math., 8:4 (2021), 45–61
K. V. Perevozhikova, N. A. Manakova, “Chislennoe modelirovanie startovogo upravleniya i finalnogo nablyudeniya v modeli filtratsii zhidkosti”, J. Comp. Eng. Math., 8:1 (2021), 29–45
K. V. Vasiuchkova, “Chislennoe issledovanie dlya zadachi startovogo upravleniya i finalnogo nablyudeniya v modeli raspredeleniya potentsialov v kristallicheskom poluprovodnike”, J. Comp. Eng. Math., 6:3 (2019), 54–68
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