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Uspekhi Mat. Nauk, 2014, Volume 69, Issue 2(416), Pages 107–148 (Mi umn9579)  

This article is cited in 23 scientific papers (total in 23 papers)

Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field

A. L. Skubachevskii

Peoples Friendship University of Russia, Moscow

Abstract: This paper is concerned with the first mixed problem for the Vlasov–Poisson equations in an infinite cylinder, a problem describing\linebreak the evolution of the density distribution of ions and electrons in a high temperature plasma under an external magnetic field. A stationary solution is constructed for which the charged-particle density distributions are supported in a strictly interior cylinder. A classical solution for which the supports of the charged-particle density distributions are at a distance from the cylindrical boundary is shown to exist and to be unique in some neighbourhood of the stationary solution.
Bibliography: 127 titles.

Keywords: Vlasov–Poisson equations, mixed problem, classical solutions, homogeneous magnetic field.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-4479.2014.1
This research was carried out with the support of the Programme for the Support of Leading Scientific Schools (grant no. НШ-4479.2014.1).


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English version:
Russian Mathematical Surveys, 2014, 69:2, 291–330

Bibliographic databases:

UDC: 517.9
MSC: Primary 35Q83; Secondary 82D10, 76X05
Received: 27.10.2013

Citation: A. L. Skubachevskii, “Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field”, Uspekhi Mat. Nauk, 69:2(416) (2014), 107–148; Russian Math. Surveys, 69:2 (2014), 291–330

Citation in format AMSBIB
\by A.~L.~Skubachevskii
\paper Vlasov--Poisson equations for a two-component plasma in a~homogeneous magnetic field
\jour Uspekhi Mat. Nauk
\yr 2014
\vol 69
\issue 2(416)
\pages 107--148
\jour Russian Math. Surveys
\yr 2014
\vol 69
\issue 2
\pages 291--330

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    This publication is cited in the following articles:
    1. Knopf P., “Confined Steady States of a Vlasov-Poisson Plasma in An Infinitely Long Cylinder”, Math. Meth. Appl. Sci.  crossref  isi
    2. A. L. Skubachevskii, “Nonlocal elliptic boundary value problems in an infinite cylinder”, Dokl. Math., 91:2 (2015), 147–149  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. A. L. Skubachevskii, “Nonlocal Problems for the Vlasov–Poisson Equations in an Infinite Cylinder”, Funct. Anal. Appl., 49:3 (2015), 234–238  mathnet  crossref  crossref  isi  elib
    4. Yu. O. Belyaeva, “Statsionarnye resheniya uravnenii Vlasova dlya vysokotemperaturnoi dvukomponentnoi plazmy”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 19–31  mathnet
    5. A. L. Skubachevskii, “Nonlocal elliptic problems in infinite cylinder and applications”, Discrete Contin. Dyn. Syst. Ser. S, 9:3 (2016), 847–868  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. L. Skubachevskii, Y. Tsuzuki, “Vlasov–Poisson equations for a two-component plasma in a half-space”, Dokl. Math., 94:3 (2016), 681–683  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    7. Sh. Kondo, “An almost-periodic solution of Hasegawa-Wakatani equations with vanishing resistivity”, Proc. Roy. Soc. Edinburgh Sect. A, 146:5 (2016), 983–1003  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. L. Skubachevskii, Y. Tsuzuki, “Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space”, Comput. Math. Math. Phys., 57:3 (2017), 541–557  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Yu. Belyaeva, “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 (2017), 37–50  crossref  mathscinet  zmath  isi  scopus
    11. M. Dehghan, M. Abbaszadeh, “A local meshless method for solving multi-dimensional Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck systems arising in plasma physics”, Eng. Comput., 33:4 (2017), 961–981  crossref  isi  scopus
    12. V. V. Vedenyapin, A. A. Andreeva, V. V. Vorobyeva, “Euler and Navier–Stokes equations as self-consistent fields”, Dokl. Math., 97:3 (2018), 283–285  mathnet  crossref  crossref  zmath  isi  elib  scopus
    13. V. V. Vedenyapin, “Uravnenie Vlasova–Maksvella–Einshteina”, Preprinty IPM im. M. V. Keldysha, 2018, 188, 20 pp.  mathnet  crossref  elib
    14. 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
    15. Yu. O. Belyaeva, A. L. Skubachevskii, “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
    16. A. A. Kosov, E. I. Semenov, V. V. Tirskikh, “On exact multidimensional solutions of a nonlinear system of first order partial differential equations”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 28 (2019), 53–68  mathnet  crossref
    17. A. A. Kosov, E. I. Semenov, V. V. Tirskikh, “Mnogomernye tochnye resheniya sistemy nelineinykh uravnenii tipa Bussineska”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 114–124  mathnet  crossref
    18. V. V. Vedenyapin, I. S. Pershin, “Vlasov–Maxwell–Einstein equation and Einstein lambda”, Preprinty IPM im. M. V. Keldysha, 2019, 039, 17 pp.  mathnet  crossref
    19. V. V. Vedenyapin, N. S. Smirnova, “Uravneniya Eilera i Nave–Stoksa kak sledstviya uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2019, 041, 20 pp.  mathnet  crossref  elib
    20. Weber J., “Confined Steady States of the Relativistic Vlasov-Maxwell System in An Infinitely Long Cylinder”, Kinet. Relat. Mod., 13:6 (2020), 1135–1161  crossref  mathscinet  zmath  isi
    21. Rozanova O.S., Chizhonkov E.V., “On the Conditions For the Breaking of Oscillations in a Cold Plasma”, Z. Angew. Math. Phys., 72:1 (2021), 13  crossref  mathscinet  isi
    22. A. A. Kosov, E. I. Semenov, V. V. Tirskikh, “O tochnykh mnogomernykh resheniyakh odnoi nelineinoi sistemy giperbolicheskikh uravnenii chetvertogo poryadka”, Sib. zhurn. industr. matem., 24:2 (2021), 77–86  mathnet  crossref
    23. A. A. Kosov, E. I. Semenov, “O suschestvovanii periodicheskikh reshenii odnoi nelineinoi sistemy parabolicheskikh uravnenii chetvertogo poryadka”, Differentsialnye uravneniya i optimalnoe upravlenie, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 196, VINITI RAN, M., 2021, 98–104  mathnet  crossref
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