Stability aspects in a nonsimple thermoelastic diffusion problem

References

• Mindlin , RD . 1964 . Micro-structure in linear elasticity . Arch. Ration. Mech. Anal. , 16 : 51 – 78 .
   Web of Science ®Google Scholar
• Toupin , RA . 1964 . Theories of elasticity with couple-stress . Arch. Ration. Mech. Anal. , 17 : 85 – 112 .
   Web of Science ®Google Scholar
• Ciarletta , M and Ieşan , D . 1993 . “ Non-classical Elastic Solids ” . In Pitman Research Notes in Mathematical Series , Vol. 293 , New York : John Wiley & Sons, Inc. .
   Google Scholar
• Green , AE and Rivlin , RS . 1964 . Multipolar continuum mechanics . Arch. Ration. Mech. Anal. , 17 : 113 – 147 .
   Web of Science ®Google Scholar
• Ieşan , D . 2004 . Thermoelastic Models of Continua , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Ieşan , D and Quintanilla , R . 1992 . On the grade consistent theory of micropolar thermoelasticity . J. Therm. Stresses , 15 : 393 – 417 .
   Web of Science ®Google Scholar
• Kolakowski , H and Lazuka , J . 2008 . The Cauchy problem for the system of partial differential equations describing nonsimple thermoelasticity . Appl. Math. , 35 : 97 – 105 .
   Google Scholar
• Pata , V and Quintanilla , R . 2010 . On the decay of solutions in nonsimple elastic solids with memory . J. Math. Anal. Appl. , 363 : 19 – 28 .
   Web of Science ®Google Scholar
• Fernàndez Sare , HD , Munoz Rivera , JE and Quintanilla , R . 2010 . Decay of solutions in nonsimple thermoelastic bars . Int. J. Eng. Sci. , 48 : 1233 – 1241 .
   Web of Science ®Google Scholar
• Aouadi , M . 2011 . Exponential stability in hyperbolic thermoelastic diffusion problem with second sound . Int. J. Diff. Eqns , 2011 : 1 – 21 .
   Google Scholar
• Aouadi , M . 2011 . “ Exponential stability in the theory of thermoelastic diffusion mixtures ” . In Appl. Anal. DOI: 10.1080/00036811.2011.596478
   Google Scholar
• Aouadi , M . 2012 . Stability in thermoelastic diffusion theory with voids . Appl. Anal. , 91 : 121 – 139 .
   Web of Science ®Google Scholar
• Aouadi , M and Soufyane , A . 2010 . Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory . Appl. Anal. , 89 : 935 – 948 .
   Web of Science ®Google Scholar
• Aouadi , M . 2008 . Generalized theory of thermoelastic diffusion for anisotropic media . J. Thermal Stresses , 31 : 270 – 285 .
   Web of Science ®Google Scholar
• Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differential Equations , New York : Springer-Verlag .
   Google Scholar
• Prüss , J . 1984 . On the spectrum of C 0-semigroups . Trans. Am. Math. Soc. , 284 : 847 – 857 .
   Web of Science ®Google Scholar
• Liu , Z and Zheng , S . 1999 . “ Semigroups Associated to Dissipative Systems ” . In Research Notes in Mathematics , Vol. 398 , Bocca Raton , , FL : Chapman & Hall/CRC .
   Google Scholar