Publication Cover
Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 5
170
Views
4
CrossRef citations to date
0
Altmetric
Articles

Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound

, &
Pages 911-935 | Received 18 Jan 2013, Accepted 29 Apr 2013, Published online: 04 Jun 2013

References

  • Cattaneo C. Sulla conduzione del calore. Atti del Seminario Matematico e Fisico dell’Università di Modena. 1948;3(83):83–101.
  • Chandrasekharaiah DS. Thermoelasticity with second sound: a review. Applied Mechanics Review. 1986;39(3):355–376.
  • Chandrasekharaiah DS. Hyperbolic thermoelasticity: a review of recent literature. Applied Mechanics Review. 1998;51:705–729.
  • Joseph L, Preziosi DD. Heat waves. Reviews of Mod Physics. 1989;61:41–73.
  • Straughan B. Heat waves. Applied mathematical sciences. New York: Springer; 2011.
  • Racke R, Wang Y-G. Nonlinear well-posedness and rates of decay in thermoelasticity with second sound. Journal of Hyperbolic Differential Equations. 2008;5(1):25–43.
  • Tarabek MA. On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound. Quarterly of Applied Mathematics. 1992;50(4):727–742.
  • Yang L, Wang Y-G. Lp–Lq decay estimates for the Cauchy problem of linear thermoelastic systems with second sound in one space variable. Quarterly of Applied Mathematics. 2006;64(1):1–15.
  • Lax PD. Development of singularities of solutions of nonlinear hyperbolic partial differential equations. Journal of Mathematical Physics. 1964;5:611–613.
  • Hrusa WJ, Messaoudi SA. On formation of singularities on one-dimensional nonlinear thermoelasticity. Archive for Rational Mechanics and Analysis. 1990;111:135–151.
  • Dafermos CM, Hsiao L. Development of singularities in solutions of the equations of nonlinear thermoelasticity. Quarterly of Applied Mathematics. 1986;44(3):463–474.
  • Hu Y, Racke R. Formation of singularities in one-dimensional thermoelasticity with second sound. Quarterly of Applied Mathematics, in press.
  • Nirenberg L. On elliptic partial differential equations. Annali della Scuola Normale Superiore Pisa. 1959;13(3):115–162.
  • Hosono T, Kawashima S. Decay property of regularity-loss type and application to some nonlinear hyperbolic–elliptic system. Mathematical Models and Methods in Applied Sciences. 2006;16:1839–1859.
  • Matsumura A. On the asymptotic behavior of solutions of semi-linear wave equations. Publications of the Research Institute of Mathematical Sciences. 1976;12(1):169–189.
  • Segal IE. Dispersion for non-linear relativistic equations, ii. Annales Scientifique de l’École Normale Supérieure. 1968;1(4):459–497.
  • Shizuta Y, Kawashima S. Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation. Hokkaido Mathematics Journal. 1985;14:249–275.
  • Beauchard K, Zuazua E. Large time asymptotics for partially dissipative hyperbolic systems. Archive for Rational Mechanics and Analysis. 2011;199(1):177–227.
  • Said-Houari B, Kasimov A. Decay property of Timoshenko system in thermoelasticity. Mathematical Methods in the Applied Sciences. 2012;35(3):314–333.
  • Racke R, Said-Houari B. Decay rates and global existence for semilinear dissipative Timoshenko systems. Quart. Appl. Math. in press.
  • Racke R, Said-Houari B. Global existence and decay property of the Timoshenko system in thermoelasticity with second sound. Nonlinear Analysis, T.M.A. 2012;75:4957–4973.
  • Ikehata R. Decay estimates by moments and masses of initial data for linear damped wave equations. International Journal of Pure and Applied Mathematics. 2003;5(1):77–94.
  • Ikehata R. New decay estimates for linear damped wave equations and its application to nonlinear problem. Mathematical Methods in Applied Sciences. 2004;27(8):865–889.
  • Bianchini S, Hanouzet B, Natalini R. Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy. Communications in Pure and Applied Mathematics. 2007;60(11):1559–1622.
  • Slemrod M. Global existence, uniqueness, and asymptotic stability of classical solutions in one-dimensional thermoelasticity. Archives for Rational Mechanics and Analysis. 1981; 76.
  • Ide K, Kawashima S. Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system. Mathematical Models and Methods in Applied Sciences. 2008;18(7): 1001–1025.
  • Racke R. Lectures on nonlinear evolution equations. Initial value problems. Aspects of mathematics. Braunschweig: Friedrich Vieweg and Sohn; 1992.

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.