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

摘要

In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations: u(tt) + Delta(2)u + Delta theta = 0 and theta(t) - Delta theta - Delta u(t) = 0 in Omega x (0, infinity). subject to Dirichlet boundary conditions: u vertical bar Gamma = D(v)u vertical bar Gamma = theta vertical bar Gamma = 0 and initial conditions (u, u(t), theta)vertical bar(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 F of which is assumed to be a C-4-hypersurface.