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

Robert Denk, Reinhard Racke, Yoshihiro Shibata

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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) ∈ W2p,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 W2P,D by the formula W2P,D = {u ∈ W2p: 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 Dec 1

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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