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:

subject to Dirichlet boundary conditions: $u{|}_{\Gamma }=D_{\nu }u{|}_{\Gamma }=\theta {|}_{\Gamma }=0$ and initial conditions $(u,u_t,\theta ){|}_{t=0}=(u_0,v_0,{\theta }_0)$. Here $\Omega$ is an exterior domain (domain with bounded complement) in $R^n$ with $n=2$ or $n=3$, the boundary $\Gamma$ of which is assumed to be a $C^4$-hypersurface.