Applied Mathematics and Mechanics

, Volume 29, Issue 2, pp 259–262

Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms

  • Xu Run-zhang  (徐润章)
  • Zhao Xi-ren  (赵希人)
  • Shen Ji-hong  (沈继红)
Article

DOI: 10.1007/s10483-008-0213-y

Cite this article as:
Xu, R., Zhao, X. & Shen, J. Appl. Math. Mech.-Engl. Ed. (2008) 29: 259. doi:10.1007/s10483-008-0213-y

Abstract

This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite, under a very simple and mild assumption regarding the nonlinear term.

Key words

fourth order wave equation dispersive dissipative asymptotic behaviour 

Chinese Library Classification

O175.26 

2000 Mathematics Subject Classification

35L70 

Copyright information

© Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008

Authors and Affiliations

  • Xu Run-zhang  (徐润章)
    • 1
    • 2
  • Zhao Xi-ren  (赵希人)
    • 2
  • Shen Ji-hong  (沈继红)
    • 2
  1. 1.College of ScienceHarbin Engineering UniversityHarbinP. R. China
  2. 2.College of AutomationHarbin Engineering UniversityHarbinP. R. China