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

Robert Denk, Reinhard Racke, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Local Energy Decay
    Plate Equation
    Decay Estimates
    Exterior Domain
    Energy Estimates
    Thermoelastic
    Resolvent
    Dirichlet Boundary Conditions
    Hypersurface
    Initial conditions
    Complement
    Boundary conditions
    Three-dimensional

    Keywords

    • Energy estimates
    • Resolvent expansion
    • Thermoelastic plate equations

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

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    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.",
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    AU - Denk, Robert

    AU - Racke, Reinhard

    AU - Shibata, Yoshihiro

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    Y1 - 2010

    N2 - 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.

    AB - 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.

    KW - Energy estimates

    KW - Resolvent expansion

    KW - Thermoelastic plate equations

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