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Acta Mathematicae Applicatae Sinica, English Series

, Volume 19, Issue 3, pp 477–484 | Cite as

The Global Existence of One Type of Nonlinear Kirchhoff String Equation

Original papers

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.

Keywords

Kirchhoff equation global well-posedness 

2000 MR Subject Classification

35L70 35B10 37L10 

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References

  1. 1.
    Frota, C.L., Goldstein, J.A. Some nonlinear wave equations with acoustic boundary conditions. Diff. Equ. J., 164:92–109 (2000)MathSciNetCrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Ikehata, R. Some remarks on the wave equations with nonlinear damping and source terms. Non. Anal. Theo. Meth. Appl., 27:1165–1175 (1996)CrossRefGoogle Scholar
  4. 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. 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)MathSciNetCrossRefGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    Lions, J.L. Quelques m´ethodes de r´esolution des probl`emes aux limites non–lin´eaires. Dunod, Paris, 1969Google Scholar
  8. 8.
    Miao, C., Zhang, B. The Cauchy problem for the semilinear parabolic equations in Besov spaces. Houston J. Math., (2003), to appearGoogle Scholar
  9. 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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Beijing Graduate School of ChinaAcademy of Engineering PhysicsBeijingChina

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