66
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Optimal Decay Rate for Unidimensional Thermoelastic Problem within the Green-Lindsay Model

&
Pages 1199-1216 | Received 03 Dec 2014, Accepted 13 May 2015, Published online: 01 Sep 2015

REFERENCES

  • H. Lord and Y. Shulman , A Generalized Dynamical Theory of Thermoelasticity , J. Mech. Phys. Solids , vol. 15 , pp. 299 – 309 , 1967 .
  • A. E. Green and K. E. Lindsay , Thermoelasticity , J. Elastic. , vol. 2 , pp. 1 – 7 , 1972 .
  • R. B. Hetnarski and J. Ignaczak , Generalized Thermoelasticity , J. Thermal Stresses , vol. 22 , pp. 451 – 476 , 1999 .
  • S. Jiang and R. Racke , Evolution Equations in Thermoelasticity. π Monographs Surveys Pure Appl. Math. Vol. 112 , Chapman & Hall/CRC , Boca Raton , 2000 .
  • S. Jiang , J. E. M. Rivera , and R. Racke , Asymptotic Stability and Global Existence in Thermoelasticity with Symmetry , Quart. Appl. Math. , vol. 56 , pp. 259 – 275 , 1998 .
  • M. O. Rieger , Exponential Stability and Global Existence in Thermoelasticity with Radial Symmetry , Quart. Appl. Math. , vol. 62 , pp. 1 – 25 , 2004 .
  • W. J. Liu , Partial Exact Controllability and Exponential Stability of the Higher Dimensional Linear Thermoelasticity , ESAIM: Cont. Opt. Cal. Var. , vol. 3 , pp. 23 – 48 , 1998 .
  • Z. Liu and S. Zheng , On the Exponential Stability of Linear Viscoelasticity and Thermoviscoelasticity , Quart. Appl. Math. , vol. 54 , pp. 21 – 31 , 1996 .
  • T. Irmscher , Zur Asymptotik Thermoelastischer Systeme mit Second Sound, Staatsexamensarbeit, Univ. Konstanz, 2003.
  • T. Irmscher , Rate of Stability in Hyperbolic Thermoelasticity , Konst. Sch. Math. Inf. , vol. 214 , pp. 1 – 15 , 2006 .
  • T. Irmscher , and R. Racke , Sharp Decay Rates in Parabolic, and Hyperbolic Thermoelasticity , IMA J. Appl. Math. , vol. 71 , pp. 459 – 478 , 2006 .
  • R. Racke , Thermoelasticity with Second Sound Exponential Stability in Linear and Nonlinear 1-d , Math. Mod. Meth. Appl. Sci. , vol. 25 , pp. 409 – 441 , 2002 .
  • R. Racke , Asymptotic Behavior of Solutions in Linear 2- or 3-d Thermoelasticity with Second Sound , Quart. Appl. Math. , vol. 61 , pp. 315 – 328 , 2003 .
  • X. Zhang , and E. Zuazua , Decay of Solutions of the System of Thermoelasticity of Type III , Commun. Contem. Math. , vol. 5 , pp. 25 – 83 , 2003 .
  • M. Aouadi and A. Soufyane , Polynomial and Exponential Stability for One-Dimensional Problem in Thermoelastic Diffusion Theory , Appl. Anal. , vol. 89 , pp. 935 – 948 , 2010 .
  • M. Aouadi , Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem , Int. J. Diff. Equat. , vol. 2011 , pp. 1 – 21 , 2011 .
  • M. Aouadi , Generalized Three Dimensional Heat Source Problem for Small Time , Int. J. Comput. Meth. Engin. Sci. Mech. , vol. 7 , pp. 59 – 67 , 2006 .
  • A. Magana , and R. Quintanilla , On the Exponential Decay of Solutions in One Dimensional Generalized Porous-Thermo-Elasticity , Asym. Anal. , vol. 49 , pp. 173 – 187 , 2006 .
  • M. Aouadi , Some Theorems in the Generalized Theory of Thermo-Magnetoelectroelasticity under Green-Lindsay's Model , Acta Mech. , vol. 200 , pp. 25 – 43 , 2008 .
  • M. I. M. Copetti , and M. Aouadi , Analysis of a Contact Problem in Thermoviscoelasticity Under the Green-Lindsay Model , Appl. Num. Math. , vol. 91 , pp. 60 – 74 , 2015 .
  • N. Sumi , Numerical Solutions of Thermoelastic Wave Problems by the Method of Characteristics , J. Thermal Stresses , vol. 24 , pp. 509 – 530 , 2001 .
  • D. V. Strunin , R. V. N. Melnik , and A. J. Roberts , Coupled Thermomechanical Waves in Hyperbolic Thermoelasticity , J. Thermal Stresses , vol. 24 , pp. 121 – 140 , 2001 .
  • Efunda, Inc., The Ultimate Online Reference for Engineers, 2002, www.efunda.com.
  • C. Heilmann , The Chemlab Server, 2002, http://chemlab.pc.maricopa.edu/periodic/ default.html.
  • Ioffe Physical-Technical Institute, Physical Properties of Semiconductors, 2002, http://www.ioffe.ru/SVA/NSM/Semicond/.
  • D. S. Chandrasekharaiah , Thermoelasticity with Second Sound: A Review , Appl. Mech. Rev. , vol. 39 , pp. 355 – 376 , 1986 .
  • R. Quintanilla , and R. Racke , Stability in Thermoelasticity of Type III , Disc. Cont. Dyn. Syst.-Seri. B , vol. 3 , pp. 383 – 400 , 2003 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.