Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Asymptotic stability in nonlinear viscoelasticity


Authors: C. E. Beevers and M. Šilhavý
Journal: Quart. Appl. Math. 42 (1984), 281-294
MSC: Primary 73F99
DOI: https://doi.org/10.1090/qam/757166
MathSciNet review: 757166
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we present sufficient conditions for asymptotic stability of a homogeneous equilibrium state of a (nonlinear) elastic body with linear viscosity. The body is subject to external conditions of zero displacements on a part of the boundary, zero surface tractions on the remaining part of the boundary and zero body forces in the interior of the body. The meaning and further qualitative consequence of our conditions are also discussed.


References [Enhancements On Off] (What's this?)

  • [1] R. J. Knops and E. W. Wilkes, Theory of elastic stability, Handbuch der Physik VIa/3, Springer-Verlag, Berlin and New York, 1973
  • [2] Morton E. Gurtin, Thermodynamics and stability, Arch. Rational Mech. Anal. 59 (1975), no. 1, 63–96. MR 0479061, https://doi.org/10.1007/BF00281517
  • [3] Constantine M. Dafermos, Can dissipation prevent the breaking of waves?, Transactions of the Twenty-Sixth Conference of Army Mathematicians (Hanover, N.H., 1980) ARO Rep. 81, vol. 1, U. S. Army Res. Office, Research Triangle Park, N.C., 1981, pp. 187–198. MR 605324
  • [4] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972 (French). Travaux et Recherches Mathématiques, No. 21. MR 0464857
  • [5] C. C. Wang and C. Truesdell, Introduction to rational elasticity, Noordhoff International Publishing, Leyden, 1973. Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics of Continua. MR 0468442
  • [6] John M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), no. 4, 337–403. MR 0475169, https://doi.org/10.1007/BF00279992
  • [7] C. Truesdell, A first course in rational continuum mechanics, The Johns Hopkins University, Maryland, 1972
  • [8] J. Nečas and J. Hlavaček, Mathematical theory of elastic and elasto-plastic bodies: An introduction, Elsevier, Amsterdam, Oxford, New York, 1981
  • [9] C. B. Morrey, Multiple integrals in the calculus of variations, Springer, Berlin, 1966
  • [10] A. Kufner, O. John and S. Fučík, Function space, Praha, Academia, Noørdhoff, 1977

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DOI: https://doi.org/10.1090/qam/757166
Article copyright: © Copyright 1984 American Mathematical Society


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