Skip to main content
SpringerLink
Log in

The Global Existence of One Type of Nonlinear Kirchhoff String Equation

  • Original papers
  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, the global well-posedness of initial-boundary value problem to the nonlinear Kirchhoff equation with source and damping term is established by energy method.

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

  1. Frota, C.L., Goldstein, J.A. Some nonlinear wave equations with acoustic boundary conditions. Diff. Equ. J., 164:92–109 (2000)

    Article  MathSciNet  Google Scholar 

  2. Georgiev, V., Todorova, G. Existence of a solution of the wave equation with nonlinear damping and source terms. Diff. Equ. J., 109:295–308 (1994)

    Article  Google Scholar 

  3. Ikehata, R. Some remarks on the wave equations with nonlinear damping and source terms. Non. Anal. Theo. Meth. Appl., 27:1165–1175 (1996)

    Article  Google Scholar 

  4. Levine, H.A. Instability and nonexistence of global solutions to nonlinear wave equation of the form Pu tt = −Au + F(∏). Tran. Ame. Math. Soc., 192:1–21 (1974)

    Google Scholar 

  5. Levine, H.A., Park, S.R. Global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation. J. Math. Anal. Appl., 228:181–203 (1998)

    Article  MathSciNet  Google Scholar 

  6. Levine, H.A., Park, S.R., Serrin, J. Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type. J. Diff. Equ., 142:212–219 (1998)

    Article  Google Scholar 

  7. Lions, J.L. Quelques m´ethodes de r´esolution des probl`emes aux limites non–lin´eaires. Dunod, Paris, 1969

  8. Miao, C., Zhang, B. The Cauchy problem for the semilinear parabolic equations in Besov spaces. Houston J. Math., (2003), to appear

  9. Ono, K. On global solutions and blow up solutions of nonlinear Kirchhoff strings with nonlinear dissipation. J. Math. Anal. Appl., 216:321–342 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beijing Graduate School of China, Academy of Engineering Physics, Beijing, 100088, China

    Xiao-yi Zhang

Authors
  1. Xiao-yi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-yi Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Xy. The Global Existence of One Type of Nonlinear Kirchhoff String Equation. Acta Mathematicae Applicatae Sinica, English Series, English Series 19, 477–484 (2003). https://doi.org/10.1007/s10255-003-0123-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-003-0123-1

Keywords

2000 MR Subject Classification

Search

Navigation