References
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- J. Carr, Applications of centre manifold theory, Springer-Verlag New York, Inc., 1981. MR 635782 (83g:34039)
- C. M. Dafermos, Contemporary issues in the dynamic behaviour of continuous media, LCDS Lecture Notes, Brown University, vol. 85–1, 1985.
- J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag New York, Inc., 1983. MR 709768 (85f:58002)
- B. L. Keyfitz and H. C. Kranzer, Non-strictly hyperbolic systems of conservation laws: formation of singularities, Contemporary Math., 17 (1983), pp. 77–90. MR 706089 (84h:35102)
- B. L. Keyfitz and C. A. Mora, Prototypes for nonstrict hyperbolicity in conservation laws, Contemp. Math., Amer. Math. Soc., 255 (2000), pp. 125–137. MR 1752505 (2001d:35132)
- R. J. Knops, H. A. Levine and L. E. Payne, Nonexistence, instability and growth theorems for solutions to an abstract nonlinear equation with applications to elastodynamics, Arch. Rational Mech. Anal., 55 (1974), pp. 52–72. MR 0364839 (51:1093)
- H. A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal., 5 (1974), pp. 138–146. MR 0399682 (53:3525)
- H. Li and K. Saxton, Asymptotic behavior of solutions to quasilinear hyperbolic equations with nonlinear damping, Quart. Appl. Math., 61 (2003), pp. 295–313. MR 1976371 (2004f:35112)
- T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Publications Mathématiques d’Orsay, 78.02 (1978), Dépt. de Mathématique, Paris-Sud. MR 0481578 (58:1690)
- T. Ruggeri, A. Muracchini, and L. Seccia, Shock waves and second sound in a rigid heat conductor: A critical temperature for NaF and Bi, Phys. Rev. Lett., 64 (1990), pp. 2640–2643.
- K. Saxton and R. Saxton, Nonlinearity and memory effects in low temperature heat propagation, Arch. Mech., 52 (2000), pp. 127–142.
- K. Saxton and R. Saxton, Phase transitions and aspects of heat propagation in low temperature solids, Proceedings from the International Conference on Differential Equations Hasselt, (EQUADIFF 2003), eds. F. Dumortier et al., World Scientific, 2005, pp. 1128–1130. MR 2185197
- R. Saxton, Blow-up at the Boundary of Solutions to Nonlinear Evolution Equations, “Evolution Equations”, eds. G. Ferreyra, G. R. Goldstein and F. Neubrander, Lecture Notes in Pure and Applied Mathematics, 168 (1994), pp. 383–392. MR 1300444 (95i:35025)
- M. Slemrod, Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity, Arch. Rat. Mech. Anal., 76 (1981), pp. 97–133. MR 629700 (83c:73056)
- Y. Wang, Finite time blow-up results for the damped wave equations with arbitrary energy in an inhomogeneous medium, Arxiv preprint math/0702190v1 (2007).