Spatial asymptotic behaviour in incremental thermoelasticity

Asymptotic Analysis

Volumn 27, Issue 3-4, 2001, Pages 265-279

  Quintanilla, R ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Incremental thermoelastodynamics; Saint Venant's principle; Spatial estimates

Indexed keywords

EID: 0035446732     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. F. Bofill and R. Quintanilla, Spatial estimates for dynamical problems in several elasticity theories, Rich. Mat. XLVI (1997), 425-441.
2. F. Bofill and R. Quintanilla, On existence and uniqueness of unbounded solutions in incremental themoelasticity, in: Thermal Stresses '99, 3rd International Congress on Thermal Stresses, J.J. Skrzypek and R.B. Hetnarski, eds, Krakow, 1999, pp. 99-102.
3. F. Bofill, F. Martinez and R. Quintanilla, Existence of solutions of the equations of incremental themoelasticity for unbounded domains, J. Thermal Stresses 18 (1995), 1-12.
4. B.A. Boley, Some observations on Saint-Venant's principle, in: 3rd US Natl. Cong. Appl. Mech., ASME, New York, 1958, pp. 259-264
5. A. Borrelli and M.C. Patria, Energy bounds for a mixture of two linear elastic solids occupying a semi-infinite cylinder, Acta Mech. 109 (1995), 191-206.
6. A. Borrelli and M.C. Patria, Energy bounds in dynamic problems for a semi-infinite magnetoelastic beam, J. Appl. Math. Phys. (ZAMP) 47 (1996), 880-893.
7. S. Chirita, Saint-Venant's principle in linear thermoelasticity, J. Thermal Stresses 18 (1995), 485-496.
8. S. Chirita, A Phragmen-Lindelof principle in dynamic linear thermoelasticity, J. Thermal Stresses 20 (1997), 505-516.
9. S. Chirita and A. Danescu, Spatial decay and growth properties for the incremental thermoelascity, J. Appl. Math. Phys. (ZAMP) 51 (2000), 39-60.
10. S. Chirita and R. Quintanilla, Saint-Venant's principle in linear elastodynamics, J. Elasticity 42 (1996), 201-215.
11. S. Chirita and R. Quintanilla, Spatial decay estimates of Saint-Venant type in generalized thermoelasticity, Internat. J. Engrg. Sci. 34 (1996), 299-311.
12. S. Chirita and R. Quintanilla, Spatial estimates in the dynamic theory of linear elastic materials with memory, European J. Mech. A/Solids 16 (1997), 723-736.
13. S. Chirita and M. Ciarletta, Time-weighted surface power function method in linear thermoelasticity, in: Thermal Stresses '99, 3rd International Congress on Thermal Stresses, J.J. Skrzypek and R.B. Hetnarski, eds, Krakow, 1999, pp. 587-590.
14. A.H. England and A.E. Green, Steady state thermoelasticity for initially stressed bodies, Philos. Trans. Roy. Soc. London Ser. A 253 (1961), 517-542.
15. J.N. Flavin, R.J. Knops and L.E. Payne, Energy bounds in dynamical problems for a semi-infinite elastic beam, in: Elasticity: Mathematical Methods and Applications, Ellis-Horwood, Chichester, 1989, pp. 101-111.
16. O.P. Galdi, R.J. Knops and S. Rionero, Asymptotic behaviour in the nonlinear elastic beam, Arch. Rat. Mech. Anal. 87 (1985), 305-318.
17. C.O. Morgan, Recent developments concerning Saint-Venant's principle: An update, Appl. Mech. Rev. 42 (1989), 295-303.
18. C.O. Horgan, Decay estimates for boundary-value problems in linear and nonlinear continuum mechanics, in: Mathematical Problems in Elasticity, R. Russo, ed., World Scientific, Singapore, 1996, pp. 48-89.
19. C.O. Horgan, Recent developments concerning Saint-Venant's principle: A second update, Appl. Mech. Rev. 49 (1996), 101-111.
20. C.O. Horgan and J.K. Knowles, Recent developments concerning Saint-Venant's principle, in: Advances in Applied Mechanics, Vol. 23, J.W. Hutchinson and T.Y. Wu, eds, Academic Press, New York, 1983, pp. 179-269.
21. C.O. Horgan, L.E. Payne and L.T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. XLII (1984), 119-127.
22. D. Iesan, Incremental equations in thermoelasticity, J. Thermal Stresses 3 (1980), 41-56.
23. D. Iesan, Thermoelasticity of initially heated bodies, J. Thermal Stresses 11 (1988), 17-38.
24. D. Iesan, Prestressed Bodies, Pitman Research Notes in Mathematics Series, Vol. 195, Longman Scientific and Technical, London, 1989.
25. D. Iesan and A. Scalia, Thermoelastic Deformations, Kluwer Academic, Dordrecht, 1996.
26. J. Ignaczak, Domain of influence results in generalized thermoelasticity - A survey, Appl. Mech. Rev. 44 (1991), 375-382.
27. R.J. Knops and L.E. Payne, A Saint-Venant principle for nonlinear elasticity, Arch. Rat. Mech. Anal. 81 (1983), 1-12.
28. R.J. Knops and E.W. Wilkes, Theory of Elastic Stability, Handbuch der Physik, C. Truesdell, ed., VIa/3, Springer, Berlin, 1973.
29. J.K. Knowles, On the spatial decay of solutions of the heat equation, J. Appl. Math. Phys. (ZAMP) 22 (1971), 1050-1056.
30. V.A. Kondratiev and O.A. Oleinik, Estimates for solutions of the Dirichlet problem for the biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity. Saint-Venant's principle, Proc. Roy. Soc. Edinburgh Sect. A 93 (1983), 327-343.
31. C.B. Navarro and R. Quintanilla, On existence and uniqueness in incremental themoelasticity, J. Appl. Math. Phys. (ZAMP) 35 (1984), 206-215.
32. O.A. Oleinik and G.A Yosifian, On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary, Math. USSR Sbornik 40 (1981), 527-548.
33. O.A. Oleinik and G.A Yosifian, On the asymptotic behaviour at infinity of solutions in linear elasticity, Arch. Rat. Mech. Anal. 78 (1982), 29-53.
34. R. Quintanilla, A spatial decay estimate for the hyperbolic heat equation, SIAM J. Math. Anal. 27 (1996), 423-435.
35. R. Quintanilla, Phragmen-Lindelof alternative in nonlinear viscoelasticity, Nonlinear Anal. 34 (1998), 7-16.
36. R. Quintanilla, End effects in thermoelasticity, Math. Methods Appl. Sci 24 (2001), 93-102.
37. R. Quintanilla, Damping of end effects in a thermoelastic theory, Appl. Math. Lett. 14 (2001), 137-141.
38. R.A. Toupin, Saint-Venant's principle, Arch. Rat. Mech. Anal. 18 (1965), 83-96.