Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Oscillations in one-dimensional elasticity with surface energy


Authors: Irene Fonseca, Jack Schaeffer and Mikhail M. Shvartsman
Journal: Quart. Appl. Math. 57 (1999), 475-499
MSC: Primary 74N15; Secondary 35B35, 35Q72, 74B20, 74D10, 74G65
DOI: https://doi.org/10.1090/qam/1704443
MathSciNet review: MR1704443
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Abstract | References | Similar Articles | Additional Information

Abstract: The characterization of the oscillatory behavior of solutions of a semilinear equation in one space dimension is obtained. In this work the model equation for a material undergoing a phase transition encompasses a surface energy term and first-order memory effects.


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

  • [A] J. P. Aubin, Un théorème de compacité, C. R. Acad. Sci. 256, 5042-5044 (1963)
  • [BHJPS] J. M. Ball, P. J. Holmes, R. D. James, R. L. Pego, and P. J. Swart, On the dynamics of fine structure, J. Nonlinear Sci. 1 (1991), no. 1, 17–70. MR 1102830, https://doi.org/10.1007/BF01209147
  • [BFS] I. Fonseca, D. Brandon, and P. Swart, Dynamics and oscillatory microstructure in a model of displacive phase transformations, Progress in partial differential equations: the Metz surveys, 3, Pitman Res. Notes Math. Ser., vol. 314, Longman Sci. Tech., Harlow, 1994, pp. 130–144. MR 1316196
  • [E] L. C. Evans, Partial Differential Equations, Berkeley Mathematics Lecture Notes, 1994
  • [L] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969 (French). MR 0259693
  • [M] Lamberto Cesari (ed.), Contributions to modern calculus of variations, Pitman Research Notes in Mathematics Series, vol. 148, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1987. Papers from the symposium marking the centenary of the birth of Leonida Tonelli held in Bologna, May 13–14, 1985. MR 894067
  • [P] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
  • [Pe] Robert L. Pego, Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability, Arch. Rational Mech. Anal. 97 (1987), no. 4, 353–394. MR 865845, https://doi.org/10.1007/BF00280411
  • [T1] L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, Boston, Mass.-London, 1979, pp. 136–212. MR 584398
  • [T2] L. Tartar, Nonlinear partial differential equations using compactness method, Report 1584, MRC, Univ. Wisconsin, 1975.
  • [TZ] L. Truskinovsky and G. Zanzotto, Ericksen's bar revisited, Preprint, 1994

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Additional Information

DOI: https://doi.org/10.1090/qam/1704443
Article copyright: © Copyright 1999 American Mathematical Society


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