Lp theory for the linear thermoelastic plate equations in bounded and exterior domains

Robert Denk, Reinhard Racke, Yoshihiro Shibata

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt + Δ2u + ΔΘ = 0 and Θt - ΔΘ - Δut =0 in Ω × (0, ∞), subject to the Dirichlet boundary condition u|r = Dvu|γ = Θ|γ = 0 and initial condition (u,ut,Θ)|t=0 = (u0,v00) ∈ W2 p,D(Ω) × Lp × Lp. Here, ω is a bounded or exterior domain in ℝn (n > 2). We assume that the boundary Γ of Ω is a C4 hypersurface and we define W2 P,D by the formula W2 P,D = {u ∈ W2 p: u|γ = Dvu|γ = 0}. We show that, for any p ∈ (l,∞), the associated semigroup {T(t)}t>o is analytic. Moreover, if fi is bounded, then {T(t)}t≥o is exponentially stable.

    Original languageEnglish
    Pages (from-to)685-715
    Number of pages31
    JournalAdvances in Differential Equations
    Volume14
    Issue number7-8
    Publication statusPublished - 2009

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    Plate Equation
    Exterior Domain
    Thermoelastic
    Dirichlet Boundary Conditions
    Hypersurface
    Bounded Domain
    Initial conditions
    Semigroup
    Boundary conditions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Lp theory for the linear thermoelastic plate equations in bounded and exterior domains. / Denk, Robert; Racke, Reinhard; Shibata, Yoshihiro.

    In: Advances in Differential Equations, Vol. 14, No. 7-8, 2009, p. 685-715.

    Research output: Contribution to journalArticle

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