Spatial behaviour of solutions of the dual-phase-lag heat equation

Mathematical Methods in the Applied Sciences

Volumn 28, Issue 1, 2005, Pages 43-57

  Horgan, C O ^a   Quintanilla, R ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Dual phase lag heat equation; Hyperbolic partial differential equation; Spatial evolution on a semi infinite cylinder; Third derivative with respect to time

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONTINUUM MECHANICS; ENERGY DISSIPATION; FOURIER TRANSFORMS; HEAT FLUX; HEAT TRANSFER; PROBLEM SOLVING;

DUAL-PHASE-LAG HEAT EQUATIONS; HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION; SPATIAL EVOLUTION ON SEMI-INFINITE CYLINDER; THIRD DERIVATIVE WITH RESPECT TO TIME;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 10844246553     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.548     Document Type: Article

References (23)

1. Chandrasekharaiah DS. Hyperbolic thermoelasticity: a review of recent literature. Applied Mechanics Reviews 1998; 51:705-729.
2. Müller I, Ruggeri T. Rational and Extended Thermodynamics. Springer: New York, 1998.
3. Jou D, Casas-Vazquez J, Lebon G. Extended Irreversible Thermodynamics. Springer: Berlin, 1996.
4. Ghaleb AF, El-Deen Mohamedein MSh. A heat conduction equation with three relaxation times. International Journal of Engineering Science 1989; 27:1367-1377.
5. Franchi F, Straughan B. Continuous dependence on the relaxation time and modelling, and unbounded growth in theories of heat conduction with finite propagation speeds. Journal of Mathematical Analysis and Applications 1994; 185:726-746.
6. Quintanilla R. Spatial bounds and growth estimates for the heat equation with three relaxation times. Mathematical Methods in the Applied Sciences 1997; 20:1335-1344.
7. Quintanilla R, Straughan B. Explosive instabilities in heat transmission. Proceedings of the Royal Society of London, Series A 2002; 458:2833-2838.
8. Tzou DY. A unified approach for heat conduction from macro to micro-scales. Journal of Heat Transfer 1995; 117:8-16.
9. Goldstein J. Semigroups of Linear Operators and Applications. Oxford University Press: Oxford, 1985.
10. Quintanilla R. Exponential stability in the dual-phase-lag heat conduction theory. Journal of Non-Equilibrium Thermodynamics 2002; 27:217-227.
11. Hetnarski RB, Ignazack J. Generalized thermoelasticity. Journal of Thermal Stresses 1999; 22:451-470.
12. Flavin JN, Rionero S. Qualitative Estimates for Partial Differential Equations. CRC Press: Boca Raton, 1996.
13. Horgan CO. Recent developments concerning Saint-Venant's principle: an update. Applied Mechanics Reviews 1989; 42:295-303.
14. Horgan CO. Recent developments concerning Saint-Venant's principle: a second update. Applied Mechanics Reviews 1996; 49:101-111.
15. Horgan CO, Knowles JK. Recent developments concerning Saint-Venant's principle. In Advances in Applied Mechanics, Hutchinson JW, Wu TY (eds), vol. 23. Academic Press, New York, 1983; 179-269.
16. Horgan CO, Payne LE, Wheeler LT. Spatial decay estimates in transient heat conduction. Quarterly of Applied Mathematics 1984; 42:119-127.
17. Bofill F, Quintanilla R. Spatial estimates for dynamical problems in several elasticity theories. Ricerche di Matematica 1997; 46:425-441.
18. Song JC. Spatial decay for solutions of Cauchy problems for perturbed heat equations. Mathematical Models and Methods in the Applied Sciences 2001; 11:797-808.
19. Ames KA, Payne LE, Schaefer PW. On a nonstandard problem for heat conduction in a cylinder. Applicable Analysis 2004; 83:125-133.
20. Horgan CO, Quintanilla R. Spatial decay of transient end effects for non-standard linear diffusion problems. IMA Journal of Applied Mathematics 2004 (in press).
21. Payne LE, Schaefer PW, Song JC. Some nonstandard problems in generalized heat conduction, 2003 (preprint).
22. Payne LE, Schaefer PW, Song JC. Some nonstandard problems in viscous flow, 2003 (preprint).
23. Flavin JN, Knops RJ, Payne LE. Decay estimates for the constrained elastic cylinder of variable cross section. Quarterly of Applied Mathematics 1989; 47:325-350.