Publication Cover
Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 1
242
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Stability in thermoelastic diffusion theory with voids

Pages 121-139 | Received 28 Feb 2010, Accepted 10 Nov 2010, Published online: 23 Feb 2011

References

  • Olesiak , ZS . 1998 . Problems of thermodiffusion of deformable solids . Mater. Sci. , 34 : 297 – 303 .
  • Nowacki , W . 1974 . Dynamical problems of thermoelastic diffusion in solids . Proc. Vib. Probl. , 15 : 55 – 64 . 129–135, 257–266
  • Aouadi , M . 2010 . Qualitative results in the theory of thermoelastic diffusion mixtures . J. Thermal Stresses , 33 : 595 – 615 .
  • Aouadi , M . 2009 . The coupled theory of micropolar thermoelastic diffusion . Acta Mech. , 208 : 181 – 203 .
  • Aouadi , M . 2009 . Theory of generalized micropolar thermoelastic diffusion under Lord-Shulman model . J. Thermal Stresses , 32 : 923 – 942 .
  • Aouadi , M . 2009 . A theory of thermoelastic diffusion materials with voids . Z. Angew. Math. Phys. , 61 : 357 – 379 .
  • Dafermos , CM . 1976 . “ Contraction semigroups and trends to equilibrium in continuum mechanics ” . In Applications of Methods of Functional Analysis to Problems in Mechanics , Edited by: Germain , P and Nayroles , B . 295 – 306 . Berlin : Springer Lectures Notes in Mathematics, Vol. 503, Springer-Verlag .
  • Slemrod , M . 1981 . Global existence, uniqueness and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity . Arch. Ration. Mech. Anal. , 76 : 97 – 133 .
  • Jiang , S and Racke , R . 2000 . Evolution Equations in Thermoelasticity , Boca Raton, FL : Chapman and Hall/CRC .
  • Lebeau , G and Zuazua , E . 1999 . Decay rates for the three-dimensional linear systems of thermoelasticity . Arch. Ration. Mech. Anal. , 148 : 179 – 231 .
  • Racke , R . 2002 . Thermoelasticity with second sound-exponential stability in linear and non-linear 1-d . Math. Methods. Appl. Sci. , 25 : 409 – 441 .
  • Quintanilla , R and Racke , R . 2003 . Stability for thermoelasticity of type III . Discrete Contin. Dyn. Syst. , 3 : 383 – 400 .
  • Zhang , X and Zuazua , E . 2003 . Decay of solutions of the system of thermoelasticity of type III . Commun. Contemp. Math. , 5 : 25 – 83 .
  • Casas , PS and Quintanilla , R . 2005 . Exponential decay in one-dimensional porous-themoelasticity . Mech. Res. Commun. , 32 : 652 – 658 .
  • Magana , A and Quintanilla , R . 2006 . On the exponential decay of solutions in one-dimensional generalized porous-thermo-elasticity . Asymptot. Anal. , 49 : 173 – 187 .
  • Magana , A and Quintanilla , R . 2007 . On the time decay of solutions in porous elasticity with quasi-static microvoids . J. Math. Anal. Appl. , 331 : 617 – 630 .
  • Rivera , JM and Quintanilla , R . 2008 . On the time polynomial decay in elastic solids with voids . J. Anal. Appl. , 338 : 1296 – 1309 .
  • Pamplona , PX , Rivera , JM and Quintanilla , R . 2009 . Stabilization in elastic solids with voids . J. Math. Anal. Appl. , 350 : 37 – 49 .
  • Batkai , A , Engel , KJ , Prüss , J and Schnaubelt , R . 2006 . Polynomial stability of operators semigroup . Math. Nachr. , 279 : 1425 – 1440 .
  • Liu , Z and Rao , B . 2005 . Characterization of polynomial decay for the solution of linear evolution equation . Z. Angew. Math. Phys. , 56 : 630 – 644 .
  • Aouadi , M . 2008 . Generalized theory of thermoelastic diffusion for anisotropic media . J. Thermal Stresses , 31 : 270 – 285 .
  • Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differential Equations , New York : Springer-Verlag .
  • Prüss , J . 1984 . On the spectrum of C 0-semigroups . Trans. Am. Math. Soc. , 284 : 847 – 857 .
  • Aouadi , M and Soufyane , A . 2010 . Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory . Appl. Anal. , 89 : 935 – 948 .

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.