Comparison arguments and decay estimates in non-linear viscoelasticity

International Journal of Non-Linear Mechanics

Volumn 39, Issue 1, 2004, Pages 55-61

  Quintanilla, Ramon ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Comparison arguments; Evolution equations; Non linear viscoelasticity; Spatial estimates

Indexed keywords

DEFORMATION; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; POLYNOMIALS; VISCOELASTICITY;

NON-LINEAR VISCOELASTICITY;

NONLINEAR SYSTEMS;

EID: 0037475214     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00127-0     Document Type: Article

References (17)

1. Ames K.A., Payne L.E. Asymptotic behavior for two regularizations of the Cauchy problem for the backward heat equation. Math. Model Methods Appl. Sci. 8:1998;187-202.
2. Bofill F., Quintanilla R. Spatial estimates for dynamical problems in several elasticity theories. Ricerche Math. XLVI:1997;425-441.
3. Chirita S., Quintanilla R. Saint-Venant's principle in linear elastodynamics. J. Elasticity. 42:1996;201-215.
4. J.I. Diaz, R. Quintanilla, Spatial and continuous dependence estimates in linear viscoelasticity, J. Math. Anal. Appl. (2002), accepted for publication.
5. C.O. Horgan, J.K. Knowles, Recent developments concerning Saint-Venant's principle, In: J.W. Hutchinson, T.Y. Wu (Eds.), Advances in Applied Mechanics, Vol. 23, Academic Press, New York, 1983, pp. 179-269.
6. Horgan C.O. Recent developments concerning Saint-Venant's principle. an update Appl. Mech. Rev. 42:1989;295-303.
7. Horgan C.O. Anti-plane shear deformations in linear and non-linear solid mechanics. SIAM Rev. 37:1995;53-81.
8. Horgan C.O. Decay estimates for boundary-value problems in linear and non-linear continuum mechanics. Russo R. Mathematical Problems in Elasticity. 1996;48-89 World Scientific, Singapore.
9. Horgan C.O. Recent developments concerning Saint-Venant's principle. a second update Appl. Mech. Rev. 49:1996;101-111.
10. Horgan C.O., Payne L.E., Wheeler L.T. Spatial decay estimates in transient heat conduction. Q. Appl. Math. 42:1984;119-127.
11. Payne L.E., Song J.C. Phragmen-Lindelof and continuous dependence type results in generalized heat conduction. J. Appl. Math. Phys. (ZAMP). 47:1996;527-538.
12. Quintanilla R. Spatial decay estimates for hyperbolic heat equations. SIAM J. Math. Anal. 27:1996;78-91.
13. Quintanilla R. Phragmen-Lindelof alternative for linear equations of the anti-plane shear dynamic problem in viscoelasticity. Dyn. Continuous Discrete Impulsive Systems. 2:1996;423-435.
14. Quintanilla R. Phragmen-Lindelof alternative in non-linear viscoelasticity. Non-linear Anal. 34:1998;7-16.
15. Quintanilla R. End effects in thermoelasticity. Math. Methods Appl. Sci. 24:2001;93-102.
16. Quintanilla R. Damping of end effects in a thermoelasticity theory. Appl. Math. Lett. 14:2001;137-141.
17. Quintanilla R. Spatial asymptotic behaviour in incremental thermoelasticity. Asymptotic Anal. 27:2001;265-279.