Mathematische Zeitschrift

, Volume 132, Issue 3, pp 183–203

Blow-up theorems for nonlinear wave equations

  • Robert T. Glassey
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramowitz, M., Stegun, I. A.: Handbook of Mathematical Functions. New York: Dover Publications 1965.Google Scholar
  2. 2.
    Berger, M. S.: On Morse Theory and Stationary States for Nonlinear Wave Equations. Bull. Amer. math. Soc.76, 827–829 (1970).Google Scholar
  3. 3.
    Berger, M. S.: On the Existence and Structure of Stationary States for a Nonlinear Klein-Gordan Equation. J. functional Analysis9, 249–261 (1972).Google Scholar
  4. 4.
    Courant, R., Hilbert, D.: Methods of Mathematical Physics, Vols. I and II. New York: Interscience, 1966.Google Scholar
  5. 5.
    Fujita, H.: On the Blowing-up of Solutions of the Cauchy Problem foru tu+u 1+α. J. Fac. Sci., Univ. Tokyo, Sect. I A.13, 109–124 (1966).Google Scholar
  6. 6.
    Fujita, H.: On Some Nonexistence and Nonuniqueness Theorems for Nonlinear Parabolic Equations. In: Proceedings of the Symposium in Pure Mathematics. Vol. XVIII. Nonlinear Functional Analysis. Providence: Amer. math. Soc. 1968.Google Scholar
  7. 7.
    Garabedian, P. R.: Partial Differential Equations. New York: Wiley, 1967.Google Scholar
  8. 8.
    Jörgens, K.: Über die nichtlinearer Wellengleichungen der mathematischen Physik. Math. Ann.138, 179–202 (1959).Google Scholar
  9. 9.
    Jörgens, K.: Das Anfangswertproblem im Großen für eine Klasse nichtlinearer Wellengleichungen. Math. Z.77, 295–308 (1961).Google Scholar
  10. 10.
    Jörgens, K.: Nonlinear Wave Equations. Lecture Notes, Univ. of Colorado, March, 1970.Google Scholar
  11. 11.
    Kaplan, S.: On the Growth of Solutions of Quasilinear Parabolic Equations. Commun. pure appl. Math.,16, 327–330 (1963).Google Scholar
  12. 12.
    Keller, J. B.: On Solutions of Nonlinear Wave Equations. Commun. pure appl. Math.,10, 523–530 (1957).Google Scholar
  13. 13.
    Levine, H. A.: Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the formPu tt=−Au+F(u). Geneva: Battelle Advanced Studies Center, No. 62 (1972).Google Scholar
  14. 14.
    Morawetz, C. S., Strauss, W. A.: Decay and Scattering of Solutions of a Nonlinear Relativistic Wave Equation. Commun. pure appl. Math.,25, 1–31 (1972).Google Scholar
  15. 15.
    Strauss, W. A.: Decay and Asymptotics for □u=F(u). J. functional Analysis2, 409–457 (1968).Google Scholar
  16. 16.
    Strauss, W. A.: On Weak Solutions of Semilinear Hyperbolic Equations. Anais Acad. Brasil. Ci.42, 645–651 (1970).Google Scholar
  17. 17.
    Strauss, W. A.: The Energy Method in Nonlinear Partial Differential Equations. Brasil: Inst. Mat. Pura e Aplicada 1969.Google Scholar
  18. 18.
    Tsutsumi, M.: Existence and Nonexistence of Global Solutions for Nonlinear Parabolic Equations. (Manuscript).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Robert T. Glassey
    • 1
  1. 1.Dept. of MathematicsIndiana UniversityBloomingtonUSA

Personalised recommendations