Local Energy Decay Estimate of Solutions to the Thermoelastic Plate Equations in Two- and Three-Dimensional Exterior Domains

Abstract

In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations: utt + ∆2\_u\_ + ∆\_θ\_ = 0 and θt − ∆\_θ\_ − ∆\_ut\_ = 0 in Ω × (0, ∞), subject to Dirichlet boundary conditions: u|Γ = Dν u|Γ = θ|Γ = 0 and initial conditions (u, ut, θ)|t=0 = (\_u\_0, \_v\_0, θ\_0). Here Ω is an exterior domain (domain with bounded complement) in ℝ\_n with n = 2 or n = 3, the boundary Γ of which is assumed to be a \_C\_4-hypersurface.