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.