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dc.contributor.authorSaid-Houari, Belkacem
dc.contributor.authorKasimov, Aslan R.
dc.date.accessioned2015-08-03T11:13:56Z
dc.date.available2015-08-03T11:13:56Z
dc.date.issued2013-08
dc.identifier.citationSaid-Houari, B., & Kasimov, A. (2013). Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same. Journal of Differential Equations, 255(4), 611–632. doi:10.1016/j.jde.2013.04.026
dc.identifier.issn00220396
dc.identifier.doi10.1016/j.jde.2013.04.026
dc.identifier.urihttp://hdl.handle.net/10754/562881
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.
dc.publisherElsevier BV
dc.subjectCattaneo law
dc.subjectDecay rate
dc.subjectFourier law
dc.subjectHeat conduction
dc.subjectRegularity loss
dc.subjectTimoshenko system
dc.titleDamping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalJournal of Differential Equations
kaust.personSaid-Houari, Belkacem
kaust.personKasimov, Aslan R.


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