References
- Flavin JN, Knops RJ, Payne LE. Decay estimates for the constrained elastic cylinder of variable cross-section. Q. Appl. Math. 1989;47:325–350.
- Horgan CO, Payne LE, Wheeler LT. Spatial decay estimates in transient heat conduction. Q. Appl. Math. 1984;42:119–127.
- Horgan CO, Quintanilla R. Spatial decay of transient end effects in functionally graded heat conducting materials. Q. Appl. Math. 2001;59:529–542.
- Chirita S, Quintanilla R. Saint-Venant’s principle in linear elastodynamics. J. Elast. 1996;42:201–215.
- Flavin JN, Knops RJ, Payne LE. Energy bounds in dynamical problems for a semi-infinite elastic beam. In: Eason G, Ogden RW, editors. Elasticity: mathematical methods and applications. Chichester: Ellis Horwood; 1989. p. 101–111.
- Horgan CO, Quintanilla R. Spatial behaviour of solutions of the dual-phase-lag heat equations. Math. Meth. Appl. Sci. 2005;28:43–57.
- Quintanilla R. Damping of end effects in a thermoelastic theory. Appl. Math. Lett. 2001;14:137–141.
- Chirita S, Ciarletta M. Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua. Eur. J. Mech. A/Solids. 1999;18:915–933.
- Leseduarte MC, Quintanilla R. Phragmén-Lindelöf alternative for an exact heat conduction equation with delay. Commun. Pure Appl. Anal. 2013;12:1221–1235.
- Quintanilla R. Spatial estimates for an equation with a delay term. J. Appl. Math. Phys. (ZAMP). 2010;61:381–388.
- Chandrasekharaiah DS. Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 1998;51:705–729.
- Hetnarski RB, Ignaczak J. Generalized thermoelasticity. J. Therm. Stresses. 1999;22:451–470.
- Hetnarski RB, Ignaczak J. Nonclassical dynamical thermoelasticity. Int. J. Solids Struct. 2000;37:215–224.
- Ignaczak J, Ostoja-Starzewski M. Thermoelasticity with finite wave speeds. Mathematical monographs. Oxford; 2010.
- Straughan B. Heat waves. Vol. 177, Applied mathematical sciences New York (NY): Springer; 2011.
- Tzou DY. A unified approach for heat conduction from macro to micro-scales. ASME J. Heat Trans. 1995;117:8–16.
- Roy Choudhuri SK. On a thermoelastic three-phase-lag model. J. Therm. Stresses. 2007;30:231–238.
- Dreher M, Quintanilla R, Racke R. Ill posed problems in thermomechanics. Appl. Math. Lett. 2009;22:1374–1379.
- Jordan PM, Dai W, Mickens RE. A note on the delayed heat equation: instability with respect to initial data. Mech. Res. Commun. 2008;35:414–420.
- Chen PJ, Gurtin ME. On a theory of heat involving two temperatures. J. Appl. Math. Phys. (ZAMP). 1968;19:614–627.
- Chen PJ, Gurtin ME, Williams WO. A note on non-simple heat conduction. J. Appl. Math. Phys. (ZAMP). 1968;19:969–970.
- Chen PJ, Gurtin ME, Williams WO. On the thermodynamics of non-simple materials with two temperatures. J. Appl. Math. Phys. (ZAMP). 1969;20:107–112.
- Warren WE, Chen PJ. Wave propagation in two temperatures theory of thermoelaticity. Acta Mechanica. 1973;16:83–117.
- Quintanilla R. A well-posed problem for the three-dual-phase-lag heat conduction. J. Therm. Stresses. 2009;32:1270–1278.
- Horgan CO, Quintanilla R. Spatial decay of transient end effects for nonstandard linear diffusion problems, IMA. J. Appl. Math. 2005;70:119–128.
- Horgan CO, Wheeler LT. A spatial decay estimate for pseudoparbolic equations. Lett. Appl. Eng. Sci. 1975;3:237–243.
- Quintanilla R. Exponential stability and uniqueness in thermoelasticity with two temperatures. Dyn. Cont. Discrete Impul. Syst. A. 2004;11:57–68.
- Quintanilla R. On existence, structural stability, convergence and spatial behaviour in thermoelasticity with two temperatures. Acta Mechanica. 2004;68:61–73.
- Quintanilla R. Some solutions for a family of exact phase-lag heat conduction problems. Mech. Res. Commun. 2011;38:355–360.
- Quintanilla R, Jordan PM. A note on the two temperature theory with dual-phase-lag delay. Some exact solutions. Mech. Res. Commun. 2009;36:796–803.