Skip to main content
SpringerLink
Log in

The Burgers equation with periodic boundary conditions on an interval

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We study the asymptotic profile of the solutions of the Burgers equation on a finite interval with a periodic perturbation on the boundary. The equation describes a dissipative medium, and the initial constant profile therefore passes into a wave with a decreasing amplitude. In the low-viscosity case, the asymptotic profile looks like a sawtooth wave (with periodic breaks of the derivative), similar to the known Fay solution on the half-line, but it has some new properties.

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. R. D. Fay, J. Acoust. Soc. Amer., 3, 222–241 (1931).

    Article  ADS  Google Scholar 

  2. D. F. Parker, Proc. Roy. Soc. London Ser. A, 369, 409–424 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  3. O. V. Rudenko, Phys. Usp., 38, 965–989 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Samokhin, J. Geom. Phys., 8, 177–184 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  5. B. Dubrovin and M. Elaeva, Russ. J. Math. Phys., 19, 449–460 (2012); arXiv:1301.7216v1 [math-ph] (2013).

    Article  MathSciNet  Google Scholar 

  6. B. Dubrovin, Commun. Math. Phys., 267, 117–139 (2006).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State Technical University of Civil Aviation, Moscow, Russia

    A. V. Samokhin

Authors
  1. A. V. Samokhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Samokhin.

Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 188, No. 3, pp. 470–476, September, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samokhin, A.V. The Burgers equation with periodic boundary conditions on an interval. Theor Math Phys 188, 1371–1376 (2016). https://doi.org/10.1134/S0040577916090087

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577916090087

Keywords

Search

Navigation