Decay property of Timoshenko system in thermoelasticity

Handle URI:
http://hdl.handle.net/10754/561966
Title:
Decay property of Timoshenko system in thermoelasticity
Authors:
Said-Houari, Belkacem; Kasimov, Aslan R.
Abstract:
We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity-loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L 2 decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity-loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity-loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to U 0∈H s(R)∩L 1,γ(R) with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t -γ/2. © 2011 John Wiley & Sons, Ltd.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Wiley-Blackwell
Journal:
Mathematical Methods in the Applied Sciences
Issue Date:
30-Dec-2011
DOI:
10.1002/mma.1569
Type:
Article
ISSN:
01704214
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaid-Houari, Belkacemen
dc.contributor.authorKasimov, Aslan R.en
dc.date.accessioned2015-08-03T09:35:13Zen
dc.date.available2015-08-03T09:35:13Zen
dc.date.issued2011-12-30en
dc.identifier.issn01704214en
dc.identifier.doi10.1002/mma.1569en
dc.identifier.urihttp://hdl.handle.net/10754/561966en
dc.description.abstractWe investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity-loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L 2 decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity-loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity-loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to U 0∈H s(R)∩L 1,γ(R) with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t -γ/2. © 2011 John Wiley & Sons, Ltd.en
dc.publisherWiley-Blackwellen
dc.subjectdecay rateen
dc.subjectFourier lawen
dc.subjectsecond sounden
dc.subjectthermoelasticityen
dc.subjectTimoshenko systemsen
dc.titleDecay property of Timoshenko system in thermoelasticityen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalMathematical Methods in the Applied Sciencesen
kaust.authorSaid-Houari, Belkacemen
kaust.authorKasimov, Aslan R.en
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