Skip to main content
SpringerLink
Log in

Asymptotic behavior of solutions of a nonlinear diffusion equation with a source term of general form

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Literature Cited

  1. A. I. Bol'pert, Wave Solutions for Parabolic Equations [in Russian], (Preprint, Acad. of Sci. of the USSR. OIKhF), Chernogolovka (1983).

  2. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, “A study of an equation of diffusion coupled with an increase in quantity of matter and its application to a biological problem,” Byull. Mosk. Gos. Univ. (A),1, No. 6, 1–26 (1937).

    Google Scholar 

  3. Ya. I. Kanel', “On stabilization of solutions of a Cauchy problem for equations encountered in combustion theory,” Mat. Sb.,59, 245–288 (1962).

    Google Scholar 

  4. P. C. Fife and J. B. McLeod, “The approach of solutions of nonlinear diffusion equations to traveling wave solutions,” Arch. Rat. Mech. Anal.,65, No. 4, 335–361 (1977).

    Google Scholar 

  5. P. C. Fife and J. B. McLeod, “A phase plane discussion of convergence to traveling fronts nonlinear diffusion,” Arch. Rat. Mech. Anal.,75, No. 4, 281–314 (1981).

    Google Scholar 

  6. K. Uchiyama, “The behavior of solutions of some nonlinear diffusion equations for large time,” J. Math. Kyoto Univ.,18, No. 3, 453–508 (1978).

    Google Scholar 

  7. V. A. Vol'pert, Asymptotic Behavior of Solutions of a Nonlinear Diffusion Equation with a Positive Source [in Russian], (Preprint, Acad. of Sci. of the USSR. OIKhF), Chernogolovka (1983).

  8. F. Rothe, “Convergence to pushed fronts,” Rocky Mount. J. Math.,11, No. 4, 617–633 (1981).

    Google Scholar 

  9. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Math. Monograph #23, Amer. Math. Soc., Providence (1967).

    Google Scholar 

  10. V. A. Vol'pert, Asymptotic Behavior of Solutions of a Nonlinear Diffusion Equation [in Russian] (Preprint, Acad. of Sci. of the USSR. OIKhF), Chernogolovka (1984).

Download references

Authors
  1. V. A. Vol'pert
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Chernogolovka, Moscow District. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 1, pp. 35–47, January–February, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vol'pert, V.A. Asymptotic behavior of solutions of a nonlinear diffusion equation with a source term of general form. Sib Math J 30, 25–36 (1989). https://doi.org/10.1007/BF01054212

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01054212

Keywords

Search

Navigation