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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 3, Pages 536–552 (Mi zvmmf10541)  

This article is cited in 3 scientific papers (total in 3 papers)

Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space

A. L. Skubachevskiia, Y. Tsuzukib

a RUDN University, Moscow, Russia
b Hirosima Shudo University, TK9583410, I-I-I, Ozukahigashi Asaminami–ku, Hirosima, Japan

Abstract: We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently large induction of external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the halfspace. It is proved the existence and uniqueness of classical solution with the supports of charged-particle density distributions at some distance from the boundary, if initial density distributions are sufficiently small.

Key words: Vlasov–Poisson equations, mixed problem, classical solutions, external magnetic field, half-space.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1974.2014/К


DOI: https://doi.org/10.7868/S0044466917030140

Full text: PDF file (321 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:3, 541–557

Bibliographic databases:

UDC: 519.634
Received: 26.07.2016

Citation: A. L. Skubachevskii, Y. Tsuzuki, “Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 536–552; Comput. Math. Math. Phys., 57:3 (2017), 541–557

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Belyaeva Yu., “Stationary Solutions of the Vlasov Poisson System For Two-Component Plasma Under An External Magnetic Field in a Half-Space”, Math. Model. Nat. Phenom., 12:6, SI (2017), 37–50  crossref  mathscinet  zmath  isi
    2. Yu. O. Belyaeva, A. L. Skubachevskii, “Ob odnoznachnoi razreshimosti pervoi smeshannoi zadachi dlya sistemy uravnenii Vlasova–Puassona v beskonechnom tsilindre”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 47, K 85-letiyu Vsevoloda Alekseevicha SOLONNIKOVA, Zap. nauchn. sem. POMI, 477, POMI, SPb., 2018, 12–34  mathnet
    3. Belyaeva Yu.O., Skubachevskii A.L., “On Classical Solutions to the First Mixed Problem For the Vlasov-Poisson System in An Infinite Cylinder”, Dokl. Math., 99:1 (2019), 87–90  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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