L_p 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 + Δ²u + ΔΘ = 0 and Θ_t - ΔΘ - Δu_t =0 in Ω × (0, ∞), subject to the Dirichlet boundary condition u|r = Dvu|γ = Θ|γ = 0 and initial condition (u,u_t,Θ)|_t=0 = (u₀,v₀,Θ₀) ∈ W²_p,D(Ω) × L_p × L_p. 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 = D_vu|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.