Publikation: Local energy decay estimate of solutions to the thermoelastic plate equations in two- and three-dimensional exterior domains
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2010
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Zeitschrift für Analysis und ihre Anwendungen, pp. 21-62. ISSN 0232-2064. Available under: doi: 10.4171/ZAA/1396
Zusammenfassung
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.
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Fachgebiet (DDC)
510 Mathematik
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Thermoelastic plate equations, energy estimates, resolvent expansion
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DENK, Robert, Reinhard RACKE, Yoshihiro SHIBATA, 2010. Local energy decay estimate of solutions to the thermoelastic plate equations in two- and three-dimensional exterior domains. In: Zeitschrift für Analysis und ihre Anwendungen, pp. 21-62. ISSN 0232-2064. Available under: doi: 10.4171/ZAA/1396BibTex
@article{Denk2010Local-12744,
year={2010},
doi={10.4171/ZAA/1396},
title={Local energy decay estimate of solutions to the thermoelastic plate equations in two- and three-dimensional exterior domains},
issn={0232-2064},
journal={Zeitschrift für Analysis und ihre Anwendungen},
pages={21--62},
author={Denk, Robert and Racke, Reinhard and Shibata, Yoshihiro}
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<dcterms:abstract xml:lang="eng">In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations:<br /><br />utt + ∆2u + ∆θ = 0 and θt − ∆θ − ∆ut = 0 in Ω × (0, ∞),<br /><br />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.</dcterms:abstract>
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