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.