Local energy decay estimate of solutions to the thermoelastic plate equations in two- and three-dimensional exterior domains

Robert Denk, Reinhard Racke, Yoshihiro Shibata

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    11 Citations (Scopus)

    Abstract

    In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations: u tt + Δ2u + Δθ = 0 and ;θt-Δ;θ- Δut = 0 in ω × (0, ∞), subject to Dirichlet boundary conditions: u|⌈ = Dvu|⌈ = θ|⌈ = 0 and initial conditions (u, ut, θ)|t=o = (u0, v 0, θ0). Here ω is an exterior domain (domain with bounded complement) in ℝMn with n = 2 or n = 3, the boundary ⌈ of which is assumed to be a C4-hypersurface.

    Original languageEnglish
    Pages (from-to)21-62
    Number of pages42
    JournalZeitschrift fur Analysis und ihre Anwendung
    Volume29
    Issue number1
    DOIs
    Publication statusPublished - 2010

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    Keywords

    • Energy estimates
    • Resolvent expansion
    • Thermoelastic plate equations

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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