Mathematische Zeitschrift

, Volume 177, Issue 3, pp 323–340 | Cite as

Finite-time blow-up for solutions of nonlinear wave equations

  • Robert T. Glassey
Article

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References

  1. 1.
    Fujita, H.: On the Blowing-up of Solutions of the Cauchy problem foru t=Δu+u1+α. J. Fac. Sci. Univ. Tokyo Sect. IA Math.13, 109–124 (1966)Google Scholar
  2. 2.
    Glassey, R.: Blow-up Theorems for Nonlinear Wave Equations. Math. Z.132, 183–203 (1973)Google Scholar
  3. 3.
    Glassey, R.: On the blowing up of Solutions to the Cauchy problem for nonlinear Schrödinger equations. J. Mathematical Phys.18, 1794–1797 (1977)Google Scholar
  4. 4.
    John, F.: Blow-up of Solutions of Nonlinear Wave Equations in Three Space Dimensions. Manuscripta Math.28, 235–268 (1979)Google Scholar
  5. 5.
    Kato, T.: Blow-up of solutions of some nonlinear hyperbolic equations. Comm. Pure Appl. Math.32, 501–505 (1980)Google Scholar
  6. 6.
    Keller, J.: On Solutions of Nonlinear Wave Equations. Comm. Pure Appl. Math.10, 523–530 (1957)Google Scholar
  7. 7.
    Levine, H.: Instability and Nonexistence of global solutions to nonlinear wave equations of the formPu tt=−Au+F(u). Trans. Amer. Math. Soc.192, 1–21 (1974)Google Scholar
  8. 8.
    Sideris, T.: Ph. D. thesis. Bloomington: Indiana University 1981Google Scholar
  9. 9.
    Strauss, W.A.: Everywhere defined wave operators (In: Nonlinear Evolution Equations M.G. Crandall, ed.), Proceedings of a Symposium (Madison 1977), pp. 85–102. New York-San Francisco-London: Academic Press 1978Google Scholar
  10. 10.
    Watson, G.N.: A Treatise on the Theory of Bessel Functions (2nd Ed.). London: Cambridge University Press, 1962Google Scholar
  11. 11.
    Weissler, F.B.: Existence and Nonexistence of Global Solutions for a Semilinear Heat Equation. PreprintGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Robert T. Glassey
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonU.S.A.

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