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

XU Run-zhang;ZHAO Xi-ren;SHEN Ji-hong

doi:10.1007/s10483-008-0213-y

Applied Mathematics and Mechanics >

2008 , Vol. 29 >Issue 2: 259 - 262

DOI: https://doi.org/10.1007/s10483-008-0213-y

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

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1. College of Science, Harbin Engineering University, Harbin 150001, P. R. China;
2. College of Automation, Harbin Engineering University, Harbin 150001, P. R. China

Received date: 2007-08-15

Revised date: 2007-12-26

Online published: 2008-02-18

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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

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XU Run-zhang;ZHAO Xi-ren;SHEN Ji-hong . Asymptotic behaviour of solution for fourth order wave equation with dispersive and dissipative terms[J]. Applied Mathematics and Mechanics, 2008 , 29(2) : 259 -262 . DOI: 10.1007/s10483-008-0213-y

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