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

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References

  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. Glassey, R.: Blow-up Theorems for Nonlinear Wave Equations. Math. Z.132, 183–203 (1973)

    Google Scholar 

  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. John, F.: Blow-up of Solutions of Nonlinear Wave Equations in Three Space Dimensions. Manuscripta Math.28, 235–268 (1979)

    Google Scholar 

  5. Kato, T.: Blow-up of solutions of some nonlinear hyperbolic equations. Comm. Pure Appl. Math.32, 501–505 (1980)

    Google Scholar 

  6. Keller, J.: On Solutions of Nonlinear Wave Equations. Comm. Pure Appl. Math.10, 523–530 (1957)

    Google Scholar 

  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. Sideris, T.: Ph. D. thesis. Bloomington: Indiana University 1981

  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 1978

    Google Scholar 

  10. Watson, G.N.: A Treatise on the Theory of Bessel Functions (2nd Ed.). London: Cambridge University Press, 1962

    Google Scholar 

  11. Weissler, F.B.: Existence and Nonexistence of Global Solutions for a Semilinear Heat Equation. Preprint

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, Indiana, U.S.A.

    Robert T. Glassey

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  1. Robert T. Glassey
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Research supported in part by NSF MCS 77-01340

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Glassey, R.T. Finite-time blow-up for solutions of nonlinear wave equations. Math Z 177, 323–340 (1981). https://doi.org/10.1007/BF01162066

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  • DOI: https://doi.org/10.1007/BF01162066

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