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:<br /><br />utt + ∆2u + ∆θ = 0 and θt − ∆θ − ∆ut = 0 in Ω × (0, ∞),<br /><br />subject to Dirichlet boundary conditions: u|Γ = Dν u|Γ = θ|Γ = 0 and initial conditions (u, ut, θ)|t=0 = (u0, v0, θ0). Here Ω is an exterior domain (domain with bounded complement) in Rn with n = 2 or n = 3, the boundary Γ of which is assumed to be a C4-hypersurface.