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

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- Δu_t = 0 in ω × (0, ∞), subject to Dirichlet boundary conditions: u|⌈ = D_vu|⌈ = θ|⌈ = 0 and initial conditions (u, u_t, 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.