Global existence and decay property of the Timoshenko system in thermoelasticity with second sound

Handle URI:
http://hdl.handle.net/10754/562288
Title:
Global existence and decay property of the Timoshenko system in thermoelasticity with second sound
Authors:
Racke, Reinhard; Said-Houari, Belkacem
Abstract:
Our 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; ∂xkU(t); 2≤C( 1+t)-14-k2, provided that the initial datum U0∈ Hs(R)∩ L1(R). © 2012 Elsevier Ltd. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Elsevier BV
Journal:
Nonlinear Analysis: Theory, Methods & Applications
Issue Date:
Sep-2012
DOI:
10.1016/j.na.2012.04.011
Type:
Article
ISSN:
0362546X
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorRacke, Reinharden
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T09:59:30Zen
dc.date.available2015-08-03T09:59:30Zen
dc.date.issued2012-09en
dc.identifier.issn0362546Xen
dc.identifier.doi10.1016/j.na.2012.04.011en
dc.identifier.urihttp://hdl.handle.net/10754/562288en
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 asen
dc.description.abstract∂xkU(t)en
dc.description.abstract2≤C( 1+t)-14-k2, provided that the initial datum U0∈ Hs(R)∩ L1(R). © 2012 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.subjectDecay rateen
dc.subjectRegularity-lossen
dc.subjectSecond sounden
dc.subjectThermoelasticityen
dc.subjectTimoshenko systemsen
dc.titleGlobal existence and decay property of the Timoshenko system in thermoelasticity with second sounden
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalNonlinear Analysis: Theory, Methods & Applicationsen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germanyen
kaust.authorSaid-Houari, Belkacemen
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