Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2011 (2011), Article ID 274843, 21 pages
http://dx.doi.org/10.1155/2011/274843
Research Article

Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound

Département de Mathématique, Institut Supérieur des Sciences Appliquées et de Technologie de Mateur, Route de Tabarka, Mateur 7030, Tunisia

Received 4 May 2011; Accepted 28 June 2011

Academic Editor: Sabri Arik

Copyright © 2011 Moncef Aouadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” Journal of the Mechanics and Physics of Solids, vol. 15, no. 5, pp. 299–309, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. W. Nowacki, “Dynamical problems of thermoelastic diffusion in solids I,” Bulletin de l'Académie Polonaise des Sciences Serie des Sciences Techniques, vol. 22, p. 55–64; 129–135; 257–266, 1974. View at Google Scholar
  3. H. H. Sherief, F. A. Hamza, and H. A. Saleh, “The theory of generalized thermoelastic diffusion,” International Journal of Engineering Science, vol. 42, no. 5-6, pp. 591–608, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Aouadi, “Theory of generalized micropolar thermoelastic diffusion under Lord-Shulman model,” Journal of Thermal Stresses, vol. 32, no. 9, pp. 923–942, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Aouadi, “The coupled theory of micropolar thermoelastic diffusion,” Acta Mechanica, vol. 208, no. 3-4, pp. 181–203, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Aouadi, “A theory of thermoelastic diffusion materials with voids,” Zeitschrift für Angewandte Mathematik und Physik, vol. 61, no. 2, pp. 357–379, 2010. View at Publisher · View at Google Scholar
  7. M. Aouadi, “Qualitative results in the theory of thermoelastic diffusion mixtures,” Journal of Thermal Stresses, vol. 33, no. 6, pp. 595–615, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. C. M. Dafermos, “Contraction semigroups and trends to equilibrium in continuum mechanics,” in Applications of Methods of Functional Analysis to Problems in Mechanics, P. Germain and B. Nayroles, Eds., vol. 503 of Springer Lectures Notes in Mathematics, pp. 295–306, Springer, Berlin, Germany, 1976. View at Google Scholar
  9. M. Slemrod, “Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity,” Archive for Rational Mechanics and Analysis, vol. 76, no. 2, pp. 97–133, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Jiang and R. Racke, Evolution Equations in Thermoelasticity, vol. 112 of Monographs and Surveys in Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2000.
  11. G. Lebeau and E. Zuazua, “Decay rates for the three-dimensional linear system of thermoelasticity,” Archive for Rational Mechanics and Analysis, vol. 148, no. 3, pp. 179–231, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. H. Sherief, “On uniqueness and stability in generalized thermoelasticity,” Quarterly of Applied Mathematics, vol. 44, no. 4, pp. 773–778, 1987. View at Google Scholar · View at Zentralblatt MATH
  13. M. A. Tarabek, “On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound,” Quarterly of Applied Mathematics, vol. 50, no. 4, pp. 727–742, 1992. View at Google Scholar · View at Zentralblatt MATH
  14. R. Racke, “Thermoelasticity with second sound—exponential stability in linear and non-linear 1-d,” Mathematical Methods in the Applied Sciences, vol. 25, no. 5, pp. 409–441, 2002. View at Publisher · View at Google Scholar
  15. S. A. Messaoudi and B. Said-Houari, “Exponential stability in one-dimensional non-linear thermoelasticity with second sound,” Mathematical Methods in the Applied Sciences, vol. 28, no. 2, pp. 205–232, 2005. View at Publisher · View at Google Scholar
  16. A. Soufyane, “Energy decay for porous-thermo-elasticity systems of memory type,” Applicable Analysis, vol. 87, no. 4, pp. 451–464, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. Aouadi and A. Soufyane, “Polynomial and exponential stability for one-dimensional problem in thermoelastic diffusion theory,” Applicable Analysis, vol. 89, no. 6, pp. 935–948, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. M. Aouadi, “Generalized theory of thermoelastic diffusion for anisotropic media,” Journal of Thermal Stresses, vol. 31, no. 3, pp. 270–285, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.
  20. L. Thomas, Fundamentals of Heat Transfer, Prentice-Hall, Englewood Cliffs, NJ, USA, 1980.