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: utt + 2u + = 0 and t ut = 0 in ◊ (0,1), subject to Dirichlet boundary conditions: u| = D u| = | = 0 and initial conditions (u,ut, )|t=0 = (u0,v0, 0). Here is an exterior domain (domain with bounded comple- ment) in Rn with n = 2 or n = 3, the boundary of which is assumed to be a C4- hypersurface. u(x,0) = u0(x), ut(x,0) = v0(x), (x,0) = 0(x) (x 2 ) (1.2) and Dirichlet boundary conditions