Skip to main content
SpringerLink
Log in

Remark on nonexistence of global solutions of the initial-boundary-value problem for the nonlinear Klein-Gordon equation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Sufficient conditions are given so that the solutions of the initial-boundary-value problem for the nonlinear Klein-Gordon equation do not exist for allt>0.

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

Similar content being viewed by others

References

  • Bona, J., and Saut, J. (1993). Dispersive blow-up of solutions of generalized Korteweg-de Vries equations.Journal of Differential Equations,103, 3–57.

    Google Scholar 

  • Friedman, A. (1969).Partial Differential Equations, Holt, Rinehart & Winston, New York.

    Google Scholar 

  • Glassey, R. (1973). Blow-up theorems for nonlinear wave equations,Mathematische Zeitschrift,132, 182–203.

    Google Scholar 

  • John, F. (1979). Blow-up of solutions of nonlinear wave equations in three space dimensions,Manuscripta Mathematica,28, 235–268.

    Google Scholar 

  • Kelley, P. (1965). Self-focusing of optical beams,Physical Review Letters,15, 1005–1008.

    Google Scholar 

  • Ladyzhenskaya, O., Solonnikov, V., and Ural'tseva, N. (1967).Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow [in Russian].

    Google Scholar 

  • Reed, M. (1976).Abstract Nonlinear Wave Equations, Springer-Verlag, Berlin.

    Google Scholar 

  • Tsutsumi, M. (1984). Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schrödinger equations,SIAM Journal of Mathematical Analysis,15(2), 357–366.

    Google Scholar 

  • Zakharov, V., Sobolev, V., and Synakh, V. (1971). Behaviour of light beams in nonlinear media,Soviet Physics JETP,33, 77–81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Southwestern University, Blagoevgrad, Bulgaria

    D. D. Bainov

  2. Sofia University, Sofia, Bulgaria

    E. Minchev

Authors
  1. D. D. Bainov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Minchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bainov, D.D., Minchev, E. Remark on nonexistence of global solutions of the initial-boundary-value problem for the nonlinear Klein-Gordon equation. Int J Theor Phys 35, 1269–1277 (1996). https://doi.org/10.1007/BF02084939

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02084939

Keywords

Search

Navigation