Archive for Rational Mechanics and Analysis

, Volume 96, Issue 1, pp 55–80

Blow-up of solutions of nonlinear degenerate parabolic equations

  • Avner Friedman
  • Bryce McLeod


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964 (Reprinted by Krieger, 1976).Google Scholar
  2. 2.
    A. Friedman & B. McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), 425–447.Google Scholar
  3. 3.
    O. A. Ladyzhenskaja, V. A. Solonnikov & N. N, Ural'tzeva, Linear and Quasi-Linear Equations of Parabolic Type, Transi. Math. Monograph no. 23, Amer. Math. Soc., Providence, R.I., 1968.Google Scholar
  4. 4.
    B. C. Low, Resistive diffusion of force-free magnetic fields in a passive medium, Astrophys. J. 181 (1973), 209–226.Google Scholar
  5. 5.
    B. C. Low, Resistive diffusion of force-free magnetic fields in a passive medium. II. A nonlinear analysis of the one-dimensional case, Astrophys. J. 184 (1973), 917–929.Google Scholar
  6. 6.
    B. C. Low, Nonlinear classical diffusion in a contained plasma, Phys. Fluids 25 (1982), 402–407.Google Scholar
  7. 7.
    Miranda, C., Partial Differential Equations of Elliptic Type, Second Edition, Springer-Verlag, Berlin Heidelberg New York, 1970.Google Scholar
  8. 8.
    P. A. Watterson, Force-free magnetic evolution in the reversed-field pinch, Thesis, Cambridge University, 1985.Google Scholar
  9. 9.
    F. B. Weissler, Single point blow-up for a semilinear initial value problem, J. Diff. Eqs. 55 (1984), 204–224.Google Scholar

Copyright information

© Springer-Verlag GmbH & Co. KG 1986

Authors and Affiliations

  • Avner Friedman
    • 1
    • 2
  • Bryce McLeod
    • 1
    • 2
  1. 1.Purdue UniversityLafayette
  2. 2.Oxford UniversityOxfordEngland

Personalised recommendations