Díaz Díaz, Jesús Ildefonso and Quintanilla, R.
(2002)
*Spatial and continuous dependence estimates in linear viscoelasticity.*
Journal of Mathematical Analysis and Applications, 273
(1).
pp. 1-16.
ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X02002007

## Abstract

In this paper we consider the problem determined by the anti-plane shear dynamic deformations for the linear theory of viscoelasticity. First, we prove existence of solutions of the problem determined in a semi-infinite strip. Then, we show that the rate of decay of the end effects in this problem is faster than that known for the Laplace equation. In the last section, we study the influence of the mass density on the decay of end effects.

Item Type: | Article |
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Uncontrolled Keywords: | heat-conduction; decay |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15495 |

References: | M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions, Dover, New York, 1965. S.N. Antonsev, J.I. Diaz, S.I. Shmarev, Energy Methods for Free Boundary Problems: Applications to Nonlinear PDEs and Fluid Mechanics, Birkhäuser, Boston, 2002. H. Brezis, Operateurs Maximaux Monotones, North-Holland, Amsterdam, 1973. H. Engler, Global regular solutions for the dynamic antiplane shear problem in nonlinear viscoelasticity, Math. Z. 202 (1989) 251–259. G. Galdi, S. Rionero, Weighted Energy Methods in Fluid Dynamics and Elasticity, in: Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1985. C.O. Horgan, Anti-plane shear deformations in linear and nonlinear solid mechanics, SIAM Rev. 37 (1995) 53–81. C.O. Horgan, L.E. Payne, L.T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42 (1984) 119–127. M.J. Leitman, G.M.C. Fisher, The linear theory of viscoelasticity, in: S. Flugge (Ed.), Handbuch der Physik VIa/3, Springer-Verlag, Berlin, 1997, pp. 1–123. H.A. Levine, R. Quintanilla, Some remarks on Saint-Venant's principle, Math. Methods Appl. Sci. 11 (1989) 71–77. C. Lin, L.E. Payne, The influence of domain and diffusivity perturbations on the decay of end effects in heat conduction, SIAM J. Math. Anal. 25 (1994) 1241–1258. M.H. Protter, H.F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984. R. Quintanilla, Phragmen--Lindelöf alternative for linear equations of the anti-plane shear dynamic problem in viscoelasticity, Dynamics Contin. Discrete Impulsive Systems 2 (1996) 423–436. M. Renardy, W.J. Hrusa, J.A. Nohel, Mathematical Problems in Viscoelasticity, Longman Scientific and Technical, New York, 1987. P. Rybka, Dynamical modelling of phase transitions by means viscoelasticity in many dimensions, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992) 101–138. I.S. Sokolnikoff, R.M. Redheffer, Mathematics of Physics and Modern Engineering, 2nd ed., McGraw–Hill, New York, 1966. B. Straughan, Instability, Nonexistence and Weighted Energy Methods in Fluid Dynamics and Related Theories, in: Pitman Research Notes in Mathematics, Vol. 74, Pitman, London, 1982. |

Deposited On: | 06 Jun 2012 08:05 |

Last Modified: | 06 Feb 2014 10:25 |

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