Skip to main content
SpringerLink
Log in

Existence in the large for ▭u=F(u) in two space dimensions

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

References

  1. Chadam, J.: Asymptotics for ▭u=m 2 u+G(x,t,u,u x ,u t ), I, II. Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. Ser. III.26, 33–65, 67–95 (1972)

    Google Scholar 

  2. Glassey, R. T.: Finite-time Blow-up for solutions to Nonlinear Wave Equations. Math. Z.177, 323–340 (1981)

    Google Scholar 

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

    Google Scholar 

  4. Jörgens, K.: Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen. Math. Z.77, 295–308 1961

    Google Scholar 

  5. Kato, T.: Blow-up of solutions of some nonlinear hyperbolic equations. Comm. Pure Appl. Math. (to appear)

  6. Klainerman, S.: Global Existence for nonlinear wave equations. Preprint.

  7. Reed, M.: Abstract Nonlinear Wave Equations. Lecture Notes in Mathematics507. Berlin-Heidelberg-New York:Springer 1976

    Google Scholar 

  8. Segal, I.: Nonlinear Semigroups. Ann. of Math.78, 339–364 1963

    Google Scholar 

  9. Segal, I.: Dispersion for nonlinear relativistic equations II. Ann. Sci. Ecole Norm. Sup.1, 459–497 1968

    Google Scholar 

  10. Strauss, W.: Decay and Asymptotics for ▭u=F(u). J. Functional Analysis2, 409–457, 1968

    Google Scholar 

  11. Strauss, W.: Everywhere Defined Wave Operators. In: Nonlinear Evolution Equations (M. Crandall, Ed.). Proceedings of a Symposium (Madison 1977), pp. 85–102. New York-London: Academic Press 1978

    Google Scholar 

  12. Strauss, W.: Nonlinear Invariant Wave Equations. In: Invariant Wave Equations. Proceedings of the International School of Physics (Erice 1977), pp. 197–249. Lecture notes in Physics 73. Berlin-Heidelberg-New York: Springer 1978

    Google Scholar 

  13. von Wahl, W.: Über die klassische Lösbarkeit des Cauchy-Problems für nichtlineare Wellengleichungen bei kleinen Anfangswerten und das asymptotische Verhalten der Lösungen. Math. Z.114, 281–299, 1970

    Google Scholar 

  14. von Wahl, W.: Decay Estimates for nonlinear wave equations. J. Functional Analysis9, 490–495, 1972

    Google Scholar 

  15. von Wahl, W.:L p-Decay rates for Homogeneous Wave Equations. Math. Z.120, 93–106, 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Robert T. Glassey

Authors
  1. Robert T. Glassey
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by NSF MCS 77-01340.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glassey, R.T. Existence in the large for ▭u=F(u) in two space dimensions. Math Z 178, 233–261 (1981). https://doi.org/10.1007/BF01262042

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01262042

Keywords

Search

Navigation