Local Energy Decay Estimate of Solutions to the Thermoelastic Plate Equations in Two- and Three-Dimensional Exterior Domains
Reinhard Racke
Universität Konstanz, GermanyYoshihiro Shibata
Waseda University, Tokyo, JapanRobert Denk
Universität Konstanz, Germany

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.
Cite this article
Reinhard Racke, Yoshihiro Shibata, Robert Denk, Local Energy Decay Estimate of Solutions to the Thermoelastic Plate Equations in Two- and Three-Dimensional Exterior Domains. Z. Anal. Anwend. 29 (2010), no. 1, pp. 21–62
DOI 10.4171/ZAA/1396