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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2020, Volume 13, Issue 4, Pages 48–57 (Mi vyuru570)  

Mathematical Modelling

Anisotropic solutions of a nonlinear kinetic model of elliptic type

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk

Abstract: We consider a nonlinear kinetic model described by a system of two equations in partial derivatives of the elliptic type with exponential nonlinearities. We propose to construct exact solutions of the mathematical model in the class of logarithms from quadratic functions of spatial variables. The solution coefficients of the model are found from systems of square matrix and linear vector equations. In particular, the proposed approach is used to construct anisotropic solutions to the Liouville equation, often used as a mathematical model of stationary distributions in plasma physics. We illustrate the results by a number of examples.

Keywords: kinetic model, nonlinear elliptic system, Liouville equation, matrix equations, exact solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-08-00746
20-07-00397


DOI: https://doi.org/10.14529/mmp200404

Full text: PDF file (198 kB)
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UDC: 517.957
MSC: 35J47, 35J60
Received: 15.09.2020

Citation: A. A. Kosov, E. I. Semenov, “Anisotropic solutions of a nonlinear kinetic model of elliptic type”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 13:4 (2020), 48–57

Citation in format AMSBIB
\Bibitem{KosSem20}
\by A.~A.~Kosov, E.~I.~Semenov
\paper Anisotropic solutions of a nonlinear kinetic model of elliptic type
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2020
\vol 13
\issue 4
\pages 48--57
\mathnet{http://mi.mathnet.ru/vyuru570}
\crossref{https://doi.org/10.14529/mmp200404}


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