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Research of one mathematical model of the distribution of potentials in a crystalline semiconductor

N. A. Manakova, K. V. Vasiuchkova

South Ural State University, Chelyabinsk, Russian Federation

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.

UDC: 517.9

MSC: 60H30

Received: 27.12.2018

DOI: 10.14529/mmp190213

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