Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

Handle URI:
http://hdl.handle.net/10754/562635
Title:
Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law
Authors:
Said-Houari, Belkacem
Abstract:
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Taylor & Francis
Journal:
Applicable Analysis
Issue Date:
Feb-2013
DOI:
10.1080/00036811.2011.625015
Type:
Article
ISSN:
00036811
Sponsors:
This work has been supported by KAUST.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T10:59:14Zen
dc.date.available2015-08-03T10:59:14Zen
dc.date.issued2013-02en
dc.identifier.issn00036811en
dc.identifier.doi10.1080/00036811.2011.625015en
dc.identifier.urihttp://hdl.handle.net/10754/562635en
dc.description.abstractIn 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.en
dc.description.sponsorshipThis work has been supported by KAUST.en
dc.publisherTaylor & Francisen
dc.subjectCattaneo's lawen
dc.subjectdecay rateen
dc.subjectFourier's lawen
dc.subjectregularity lossen
dc.subjectsecond sounden
dc.subjectthermoelasticityen
dc.titleDecay properties of linear thermoelastic plates: Cattaneo versus Fourier lawen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalApplicable Analysisen
kaust.authorSaid-Houari, Belkacemen
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