On the decay of solutions to the 2D Neumann exterior problem for the wave equation

Paolo Secchi, Yoshihiro Shibata

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    5 Citations (Scopus)

    Abstract

    We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

    Original languageEnglish
    Pages (from-to)221-236
    Number of pages16
    JournalJournal of Differential Equations
    Volume194
    Issue number1
    DOIs
    Publication statusPublished - 2003 Oct 10

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    Keywords

    • Asymptotic behavior
    • Decay rate
    • Exterior domain
    • Local energy decay
    • Neumann boundary condition
    • Wave equation

    ASJC Scopus subject areas

    • Analysis

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