Skip to main content
SpringerLink
Log in

On Exact Solutions of the Oskolkov–Benjamin–Bona–Mahony–Burgers Equation

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

For the Oskolkov–Benjamin–Bona–Mahony–Burgers equation with a linear source, families of exact solutions expressed in terms of elementary and special functions are constructed. It is shown that these families contain solutions growing to infinity on finite time intervals, bounded on any finite time interval (but not globally), and bounded globally in time.

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. A. G. Sveshnikov, A. B. Al’shin, M. O. Korpusov, and Yu. D. Pletner, Linear and Nonlinear Equations of the Sobolev Type (Fizmatlit, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  2. M. O. Korpusov, Blowup in Nonclassical Nonlocal Equations (Librokom, Moscow, 2011) [in Russian].

    Google Scholar 

  3. N. Hayashi, E. Kaikina, P. Naumkin, and I. Shishmarev, Asymptotics for Dissipative Nonlinear Equations (Springer, Berlin, 2006).

    MATH  Google Scholar 

  4. A. D. Polyanin, V. F. Zaitsev, and A. I. Zhurov, Methods for Solving Nonlinear Equations of Mathematical Physics and Mechanics (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  5. N. A. Kudryashov, Methods of Nonlinear Mathematical Physics (Intellekt, Dolgoprudnyi, 2010) [in Russian].

  6. A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations (Fizmatlit, Moscow, 2002; Chapman and Hall/CRC, Boca Raton, 2011).

  7. A. B. Al’shin, M. O. Korpusov, and E. V. Yushkov, “Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion,” Comput. Math. Math. Phys. 48 (5), 764–768 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. I. Aristov, “On exact solutions of a nonclassical partial differential equation,” Comput. Math. Math. Phys. 55 (11), 1836–1841 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. I. Aristov, “On exact solutions of a third-order model equation,” Collection of Papers of Young Researchers from the Faculty of Computational Mathematics and Cybernetics of Moscow State University (Maks-Press, Moscow, 2016), Vol. 13, pp. 6–16 [in Russian].

    Google Scholar 

  10. A. I. Aristov, “Estimates for the lifespan of solutions of an initial–boundary value problem for a nonlinear Sobolev equation with variable coefficient,” Differ. Equations 48 (6), 787–795 (2012).

    Article  MathSciNet  MATH  Google Scholar 

Download references

ACKNOWLEDGMENTS

This research was supported by the Program of the President of the Russian Federation for Support of Young PhDs, project no. MK-1829.2018.1.

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    A. I. Aristov

Authors
  1. A. I. Aristov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Aristov.

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

Aristov, A.I. On Exact Solutions of the Oskolkov–Benjamin–Bona–Mahony–Burgers Equation. Comput. Math. and Math. Phys. 58, 1792–1803 (2018). https://doi.org/10.1134/S0965542518110027

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542518110027

Keywords:

Search

Navigation