Publication Cover
Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 12
101
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Exponential stability in the theory of thermoelastic diffusion mixtures

Pages 2169-2187 | Received 18 Nov 2010, Accepted 03 Jun 2011, Published online: 05 Jul 2011

References

  • Truesdell , C and Toupin , R . 1960 . The Classical Field Theories , Vol. III/1 , Berlin : Springer-Verlag .
  • Kelly , P . 1964 . A reacting continuum . Int. J. Eng. Sci. , 2 : 129 – 153 .
  • Eringen , AC and Ingram , JD . 1965 . A continuum theory of chemically reacting media I . Int. J. Eng. Sci. , 3 : 197 – 212 .
  • Green , AE and Naghdi , PM . 1968 . A note on mixtures . Int. J. Eng. Sci. , 6 : 631 – 635 .
  • Muller , I . 1968 . A thermodynamic theory of mixtures of fluids . Arch. Ration. Mech. Anal. , 28 : 1 – 39 .
  • Bowen , RM and Wiese , JC . 1969 . Diffusion in mixtures of elastic materials . Int. J. Eng. Sci. , 73 : 689 – 722 .
  • Ieşan , D . 1991 . On the theory of mixtures of thermoelastic solids . J. Thermal Stresses , 14 : 389 – 408 .
  • Ieşan , D . 1996 . Existence theorems in the theory of mixtures . J. Elasticity , 42 : 145 – 163 .
  • Ieşan , D . 2006 . Continuous dependence in a nonlinear theory of viscoelastic mixtures . Int. J. Eng. Sci. , 44 : 1127 – 1145 .
  • Ieşan , D and Quintanilla , R . 1994 . Existence and continuous dependence results in the theory of interacting continua . J. Elasticity , 30 : 85 – 98 .
  • Martinez , F and Quintanilla , R . 1995 . Some qualitative results for the linear theory of binary mixtures of thermoelastic solids . Collect. Math. , 46 : 263 – 277 .
  • Passarella , F and Zampoli , V . 2007 . Some exponential decay estimates for thermoelastic mixtures . J. Thermal Stresses , 30 : 25 – 41 .
  • Pompei , A and Scalia , A . 1999 . On the dynamic theory of mixtures of thermoelastic solids . J. Thermal Stresses , 22 : 23 – 34 .
  • D'Apice , C , Tibullo , V and Chirita , S . 2005 . On the spatial behaviour in the dynamic theory of mixtures of thermoelastic solids . J. Thermal Stresses , 28 : 63 – 82 .
  • Aouadi , M . 2010 . Qualitative results in the theory of thermoelastic diffusion mixtures . J. Thermal Stresses , 33 : 595 – 615 .
  • Casas , PS and Quintanilla , R . 2005 . Exponential decay in one-dimensional porous thermo-elasticity . Mech. Res. Commun. , 32 : 652 – 658 .
  • Magana , A and Quintanilla , R . 2006 . On the time decay of solutions in one-dimensional theories of porous materials . Int. J. Solids Struct. , 43 : 3414 – 3427 .
  • Munoz-Rivera , J and Quintanilla , R . 2008 . On the time polynomial decay in elastic solids with voids . J. Math. Anal. Appl. , 338 : 1296 – 1309 .
  • Pamplona , PX , Munoz-Rivera , J and Quintanilla , R . 2009 . Stabilization in elastic solids with voids . J. Math. Anal. Appl. , 350 : 37 – 49 .
  • Aouadi , M . 2011 . Stability in thermoelastic diffusion theory with voids . Appl. Anal. , DOI:10.1080/00036811.2010.541443, 19 pages
  • Alves , MS , Munoz Rivera , JE and Quintanilla , R . 2009 . Exponential decay in a thermoelastic mixture of solids . Int. J. Solids Struct. , 46 : 1659 – 1666 .
  • Alves , MS , Munoz Rivera , JE and Sepulveda , M . 2009 . Exponential stability in thermoviscoelastic mixtures of solids . Int. J. Solids Struct. , 46 : 4151 – 4162 .
  • Alves , MS , Munoz Rivera , JE , Sepulveda , M and Vera Villagran , OP . 2009 . Analyticity of semigroups associated with thermoviscoelastic mixtures of solids . J. Thermal Stresses , 32 : 986 – 1004 .
  • Gearhart , LM . 1978 . Spectral theory for contraction semigroups on Hilbert spaces . Trans. Am. Math. Soc. , 236 : 385 – 394 .
  • Huang , FL . 1985 . Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces . Ann. Differ. Eqns , 1 : 43 – 56 .
  • Pruss , J . 1984 . On the spectrum of C 0-semigroups . Trans. Am. Math. Soc. , 284 : 847 – 857 .
  • 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 .

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.