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Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 12–34 (Mi znsl6735)  

Unique solvability of the first mixed problem for the Vlasov–Poisson system in an infinite cylinder

Yu. O. Belyaeva, A. L. Skubachevskii

Peoples' Friendship University of Russia, Moscow, Russia

Abstract: We consider the first mixed problem for the Vlasov–Poisson system in an infinite cylinder. This problem describes the kinetics of charged particles of high-temperature plasma. We show that the characteristics of the Vlasov equations do not reach the boundary of the cylinder if the external magnetic field is sufficiently large. Sufficient conditions are obtained for existence and uniqueness of the classical solution of the Vlasov–Poisson system with ions and electrons density distribution functions supported at some distance from the boundary of the cylinder.

Key words and phrases: Vlasov–Poisson equations, mixed problem, classical solutions, external magnetic field.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 17-01-00401_а


Full text: PDF file (297 kB)
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Received: 03.12.2018

Citation: Yu. O. Belyaeva, A. L. Skubachevskii, “Unique solvability of the first mixed problem for the Vlasov–Poisson system in an infinite cylinder”, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Zap. Nauchn. Sem. POMI, 477, POMI, St. Petersburg, 2018, 12–34

Citation in format AMSBIB
\Bibitem{BelSku18}
\by Yu.~O.~Belyaeva, A.~L.~Skubachevskii
\paper Unique solvability of the first mixed problem for the Vlasov--Poisson system in an infinite cylinder
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 477
\pages 12--34
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6735}


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