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

Paolo Secchi, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Decay of Solutions
    Exterior Problem
    Decay Estimates
    Neumann Problem
    Wave equations
    Wave equation
    Local Energy Decay
    Weighted Norm
    Free Space
    Neumann Boundary Conditions
    Estimate
    Asymptotic Behavior
    Boundary conditions

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

    Cite this

    On the decay of solutions to the 2D Neumann exterior problem for the wave equation. / Secchi, Paolo; Shibata, Yoshihiro.

    In: Journal of Differential Equations, Vol. 194, No. 1, 10.10.2003, p. 221-236.

    Research output: Contribution to journalArticle

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