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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 6
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Original Articles

Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory

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Pages 935-948 | Received 17 Feb 2009, Accepted 09 Feb 2010, Published online: 18 May 2010

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: I . Bull. Acad. Pol. Sci., Ser. Sci. Technol. , 22 : 55 – 64 .
  • Nowacki , W . 1974 . Dynamical problems of thermoelastic diffusion in solids: II . Bull. Acad. Pol. Sci., Ser. Sci. Technol. , 22 : 129 – 135 .
  • Nowacki , W . 1974 . Dynamical problems of thermoelastic diffusion in solids: I . Bull. Acad. Pol. Sci., Ser. Sci. Technol. , 22 : 257 – 266 .
  • Nowacki , W . 1974 . Dynamical problems of thermoelastic diffusion in elastic solids . Proc. Vib. Probl. , 15 : 105 – 128 .
  • Gawinecki , JA and Szymaniec , A . 2002 . Global solution of the Cauchy problem in nonlinear thermoelastic diffusion in solid body . Proc. Appl. Math. Mech. , 1 : 446 – 447 .
  • Gawinecki , J , Kacprzyk , P and Bar-Yoseph , P . 2000 . Initial boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermoelastic diffusion in solid body . J. Anal. Appl. , 19 : 121 – 130 .
  • Sherief , HH , Hamza , F and Saleh , H . 2004 . The theory of generalized thermoelastic diffusion . Int. J. Eng. Sci. , 42 : 591 – 608 .
  • Aouadi , M . 2007 . Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion . J. Thermal Stresses , 30 : 665 – 678 .
  • Aouadi , M . 2008 . Generalized theory of thermoelastic diffusion for anisotropic media . J. Thermal Stresses , 31 : 270 – 285 .
  • Aouadi , M . 2008 . Qualitative aspects in the coupled theory of thermoelastic diffusion . J. Thermal Stresses , 31 : 706 – 727 .
  • Aouadi , M . 2009 . Spatial stability for the quasi-static problem in thermoelastic diffusion theory . Acta Appl. Math. , 106 : 307 – 323 .
  • 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 .
  • Dafermos , CM . 1976 . Contraction semigroups and trends to equilibrium in continuum mechanics. Applications of Methods of Functional Analysis to Problems in Mechanics , Springer Lectures Notes in Mathematics Edited by: Germain , P and Nayroles , B . Vol. 503 , 295 – 306 . Berlin : 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 .
  • Quintanilla , R . 2003 . Slow decay for one-dimensional porous dissipation elasticity . Appl. Math. Lett. , 16 : 487 – 491 .
  • Casas , PS and Quintanilla , R . 2005 . Exponential stability in thermoelasticity with microtemperatures . Int. J. Eng. Sci. , 43 : 33 – 47 .
  • 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 . 2006 . On the time decay of solutions in one-dimensional theories of porous materials . Int. J. Solids Struct. , 3 : 3414 – 3427 .
  • 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 .
  • Liu , Z and Rao , B . 2005 . Characterization of polynomial decay for the solution of linear evolution equation . Z. Angew. Math. Phys. , 56 : 630 – 644 .
  • Rivera , JM and Quintanilla , R . 2008 . On the time polynomial decay in elastic solids with voids . J. Anal. Appl. , 338 : 1296 – 1309 .
  • Soufyane , A . 2008 . Energy decay for porous-thermo-elasticity systems of memory type . Appl. Anal. , 87 : 451 – 464 .
  • Thomas , L . 1980 . Fundamentals of Heat Transfer , Englewood Cliffs, NJ : Prentice-Hall .
  • Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differential Equations , New York : Springer-Verlag .

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