Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same

Handle URI:
http://hdl.handle.net/10754/562881
Title:
Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same
Authors:
Said-Houari, Belkacem; Kasimov, Aslan R.
Abstract:
We consider the Cauchy problem for the one-dimensional Timoshenko system coupled with heat conduction, wherein the latter is described by either the Cattaneo law or the Fourier law. We prove that heat dissipation alone is sufficient to stabilize the system in both cases, so that additional mechanical damping is unnecessary. However, the decay of solutions without the mechanical damping is found to be slower than that with mechanical damping. Furthermore, in contrast to earlier results of Said-Houari and Kasimov (2012) [10] and Fernández Sare and Racke (2009) [12], we find that the Timoshenko-Fourier and the Timoshenko-Cattaneo systems have the same decay rate. The rate depends on a certain number α (first identified by Santos et al., 2012 [11] in a related study in a bounded domain), which is a function of the parameters of the system. © 2013 Elsevier Inc.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Journal of Differential Equations
Issue Date:
Aug-2013
DOI:
10.1016/j.jde.2013.04.026
Type:
Article
ISSN:
00220396
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.accessioned2015-08-03T11:13:56Zen
dc.date.available2015-08-03T11:13:56Zen
dc.date.issued2013-08en
dc.identifier.issn00220396en
dc.identifier.doi10.1016/j.jde.2013.04.026en
dc.identifier.urihttp://hdl.handle.net/10754/562881en
dc.description.abstractWe consider the Cauchy problem for the one-dimensional Timoshenko system coupled with heat conduction, wherein the latter is described by either the Cattaneo law or the Fourier law. We prove that heat dissipation alone is sufficient to stabilize the system in both cases, so that additional mechanical damping is unnecessary. However, the decay of solutions without the mechanical damping is found to be slower than that with mechanical damping. Furthermore, in contrast to earlier results of Said-Houari and Kasimov (2012) [10] and Fernández Sare and Racke (2009) [12], we find that the Timoshenko-Fourier and the Timoshenko-Cattaneo systems have the same decay rate. The rate depends on a certain number α (first identified by Santos et al., 2012 [11] in a related study in a bounded domain), which is a function of the parameters of the system. © 2013 Elsevier Inc.en
dc.publisherElsevier BVen
dc.subjectCattaneo lawen
dc.subjectDecay rateen
dc.subjectFourier lawen
dc.subjectHeat conductionen
dc.subjectRegularity lossen
dc.subjectTimoshenko systemen
dc.titleDamping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the sameen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Differential Equationsen
kaust.authorSaid-Houari, Belkacemen
kaust.authorKasimov, Aslan R.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.