On Boundary Damping for a Weakly Nonlinear Wave Equation

Darmawijoyo, Darmawijoyo and Van Horssen, W.T. (2001) On Boundary Damping for a Weakly Nonlinear Wave Equation. Reports of the Department of Applied Mathematical Analysis. ISSN 1389-6520

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    Abstract

    In this paper an initial-boundary value problem for a weakly nonlinear string (or wave) equation with non-classical boundary conditions is considered. One end of the string is assumed to be �xed and the other end of the string is attached to a spring-mass-dashpot system, where the damping generated by the dashpot is assumed to be small. This problem can be regarded as a rather simple model describing oscillations of exible structures such as suspension bridges or overhead transmission lines in a wind �eld. A multiple time-scales perturbation method will be used to construct formal asymptotic approximations of the solution. It will also be shown that all solutions tend to zero for a sufficiently large value of the damping parameter.

    Item Type: Article
    Uncontrolled Keywords: wave equation, boundary damping, asymptotics, two-timescales pertur-bation method.
    Subjects: Q Science > QA Mathematics
    Divisions: Faculty of Teacher Training and Science Education > Department of Mathematics and Sciences Education > Mathematics Education
    Depositing User: Dr. Darmawijoyo Hanapi
    Date Deposited: 18 Feb 2012 19:18
    Last Modified: 18 Feb 2012 19:18
    URI: http://eprints.unsri.ac.id/id/eprint/492

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