Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
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ArticleAuthors
Said-Houari, BelkacemDate
2011-10-10Online Publication Date
2011-10-10Print Publication Date
2013-02Permanent link to this record
http://hdl.handle.net/10754/562635
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In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier's law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.Citation
Said-Houari, B. (2011). Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law. Applicable Analysis, 92(2), 424–440. doi:10.1080/00036811.2011.625015Sponsors
This work has been supported by KAUST.Publisher
Informa UK LimitedJournal
Applicable Analysisae974a485f413a2113503eed53cd6c53
10.1080/00036811.2011.625015