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

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by the formula: W 2 p,D = {u ∈ W 2 p | u|Γ = Dνu|Γ = 0}. We show that for any p ∈ (1,∞), the associated semigroup {T (t)}t≥0 is analytic. Moreover, if Ω is bounded, then {T (t)}t≥0 is exponentially stable.