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dc.contributor.authorRacke, Reinhard
dc.contributor.authorSaid-Houari, Belkacem
dc.date.accessioned2015-08-03T09:59:30Z
dc.date.available2015-08-03T09:59:30Z
dc.date.issued2012-09
dc.identifier.issn0362546X
dc.identifier.doi10.1016/j.na.2012.04.011
dc.identifier.urihttp://hdl.handle.net/10754/562288
dc.description.abstractOur main focus in the present paper is to study the asymptotic behavior of a nonlinear version of the Timoshenko system in thermoelasticity with second sound. As it has been already proved in Said-Houari and Kasimov (2012) [29], the linear version of this system is of regularity-loss type. It is well known (Hosono and Kawashima (2006) [34], Ide and Kawashima (2008) [27], Kubo and Kawashima (2009) [41]) that the regularity-loss property of the linear problem creates difficulties when dealing with the nonlinear problem. In fact, the dissipative property of the problem becomes very weak in the high frequency region and as a result the classical energy method fails. To overcome this difficulty and following Ide and Kawashima (2008) [27] and Ikehata (2002) [30], we use an energy method with negative weights to create an artificial damping which allows us to control the nonlinearity. We prove that for 0≤k≤[s2]-2 with s<8, the solution of our problem is global in time and decays as
dc.description.abstract∂xkU(t)
dc.description.abstract2≤C( 1+t)-14-k2, provided that the initial datum U0∈ Hs(R)∩ L1(R). © 2012 Elsevier Ltd. All rights reserved.
dc.publisherElsevier BV
dc.subjectDecay rate
dc.subjectRegularity-loss
dc.subjectSecond sound
dc.subjectThermoelasticity
dc.subjectTimoshenko systems
dc.titleGlobal existence and decay property of the Timoshenko system in thermoelasticity with second sound
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalNonlinear Analysis: Theory, Methods & Applications
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany
kaust.personSaid-Houari, Belkacem


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