Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III

Handle URI:
http://hdl.handle.net/10754/575691
Title:
Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III
Authors:
Rahali, Radouane; Said-Houari, Belkacem
Abstract:
In this paper, we investigate the decay property of a Timoshenko system in thermoelasticity of type III in the whole space where the heat conduction is given by the Green and Naghdi theory. Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi's theory slows down the decay of the solution. In fact we show that the L-2-norm of the solution decays like (1 + t)(-1/8), while in the case of the coupling of the Timoshenko system with the Fourier or Cattaneo heat conduction, the decay rate is of the form (1 + t)(-1/4) [25]. We point out that the decay rate of (1 + t)(-1/8) has been obtained provided that the initial data are in L-1 (R) boolean AND H-s (R); (s >= 2). If the wave speeds of the fi rst two equations are di ff erent, then the decay rate of the solution is of regularity-loss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data. In addition, by restricting the initial data to be in H-s (R) boolean AND L-1,L-gamma (R) with gamma is an element of [0; 1], we can derive faster decay estimates with the decay rate improvement by a factor of t(-gamma/4).
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Evolution Equations and Control Theory
Issue Date:
Mar-2013
DOI:
10.3934/eect.2013.2.423
Type:
Article
ISSN:
2163-2480
Sponsors:
The authors want to thank the referee for his useful remarks and for his careful reading of the proofs. The first author thanks KAUST for its support.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorRahali, Radouaneen
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-24T08:35:57Zen
dc.date.available2015-08-24T08:35:57Zen
dc.date.issued2013-03en
dc.identifier.issn2163-2480en
dc.identifier.doi10.3934/eect.2013.2.423en
dc.identifier.urihttp://hdl.handle.net/10754/575691en
dc.description.abstractIn this paper, we investigate the decay property of a Timoshenko system in thermoelasticity of type III in the whole space where the heat conduction is given by the Green and Naghdi theory. Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi's theory slows down the decay of the solution. In fact we show that the L-2-norm of the solution decays like (1 + t)(-1/8), while in the case of the coupling of the Timoshenko system with the Fourier or Cattaneo heat conduction, the decay rate is of the form (1 + t)(-1/4) [25]. We point out that the decay rate of (1 + t)(-1/8) has been obtained provided that the initial data are in L-1 (R) boolean AND H-s (R); (s >= 2). If the wave speeds of the fi rst two equations are di ff erent, then the decay rate of the solution is of regularity-loss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data. In addition, by restricting the initial data to be in H-s (R) boolean AND L-1,L-gamma (R) with gamma is an element of [0; 1], we can derive faster decay estimates with the decay rate improvement by a factor of t(-gamma/4).en
dc.description.sponsorshipThe authors want to thank the referee for his useful remarks and for his careful reading of the proofs. The first author thanks KAUST for its support.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.titleAsymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type IIIen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalEvolution Equations and Control Theoryen
dc.contributor.institutionAnnaba Univ, Dept Math, Annaba 23000, Algeriaen
kaust.authorSaid-Houari, Belkacemen
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