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Zeitschrift für Analysis und ihre Anwendungen


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Volume 29, Issue 1, 2010, pp. 21–62
DOI: 10.4171/ZAA/1396

Published online: 2010-01-04

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

Robert Denk[1], Reinhard Racke[2] and Yoshihiro Shibata[3]

(1) Universität Konstanz, Germany
(2) Universität Konstanz, Germany
(3) Waseda University, Tokyo, Japan

In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations:

utt + ∆2u + ∆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 = (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.

Keywords: Thermoelastic plate equations, energy estimates, resolvent expansion

Denk Robert, Racke Reinhard, Shibata Yoshihiro: Local Energy Decay Estimate of Solutions to the Thermoelastic Plate Equations in Two- and Three-Dimensional Exterior Domains. Z. Anal. Anwend. 29 (2010), 21-62. doi: 10.4171/ZAA/1396