Skip to main content
SpringerLink
Log in

On Classical Solutions to the First Mixed Problem for the Vlasov–Poisson System in an Infinite Cylinder

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The first mixed problem for the Vlasov–Poisson system in an infinite cylinder is considered. This problem describes the kinetics of charged particles in a high-temperature two-component plasma under an external magnetic field. For an arbitrary electric field potential and a sufficiently strong external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the cylinder. It is proved that the Vlasov–Poisson system with ion and electron distribution density functions supported at some distance from the cylinder boundary has a unique classical solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. V. V. Kozlov, Russ. Math. Surv. 63 (4), 691–726 (2008).

    Article  Google Scholar 

  2. V. P. Maslov, J. Sov. Math. 11 (1), 123–195 (1979).

    Article  Google Scholar 

  3. S. A. Nazarov and B. A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries (Nauka, Moscow, 1991; Walter de Gruyter, Berlin, 1994).

  4. J. Batt, J. Differ. Equations 25 (3), 342–364 (1977).

    Article  Google Scholar 

  5. Y. Guo, Indiana Univ. Math. J. 43 (1), 255–320 (1994).

    Article  MathSciNet  Google Scholar 

  6. H. J. Hwang and J. J. L. Velázquez, J. Differ. Equations 247 (6), 1915–1948 (2009).

    Article  Google Scholar 

  7. C. Mouhot and C. Villani, Acta Math. 207 (1), 29–201 (2011).

    Article  MathSciNet  Google Scholar 

  8. K. Pfaffelmoser, J. Differ. Equations 95 (2), 281–303 (1992).

    Article  MathSciNet  Google Scholar 

  9. J. Schäffer, Commun. Partial Differ. Equations 16 (8–9), 1313–1335 (1991).

    Article  Google Scholar 

  10. A. L. Skubachevskii, Proc. Steklov Inst. Math. 283, 197–225 (2013).

    Article  MathSciNet  Google Scholar 

  11. A. L. Skubachevskii, Russ. Math. Surv. 69 (2), 291–330 (2014).

    Article  Google Scholar 

  12. A. L. Skubachevskii and Y. Tsuzuki, Comput. Math. Math. Phys. 57 (3), 541–557 (2017).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. RUDN University, 117198, Moscow, Russia

    Yu. O. Belyaeva & A. L. Skubachevskii

Authors
  1. Yu. O. Belyaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. L. Skubachevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu. O. Belyaeva or A. L. Skubachevskii.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belyaeva, Y.O., Skubachevskii, A.L. On Classical Solutions to the First Mixed Problem for the Vlasov–Poisson System in an Infinite Cylinder. Dokl. Math. 99, 87–90 (2019). https://doi.org/10.1134/S1064562419010277

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562419010277

Search

Navigation