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Abstract and Applied Analysis
Volume 2012, Article ID 287865, 24 pages
http://dx.doi.org/10.1155/2012/287865
Research Article

A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 19 October 2011; Accepted 23 November 2011

Academic Editor: Wing-Sum Cheung

Copyright © 2012 Fushan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. G. Ciarlet, Mathematical Elasticity. Vol. III: Theory of Shells, vol. 29 of Studies in Mathematics and Its Applications, North-Holland Publishing Co., Amsterdam, The Netherlands, 2000.
  2. F. Li, “Asymptotic analysis of linearly viscoelastic shells,” Asymptotic Analysis, vol. 36, no. 1, pp. 21–46, 2003. View at Google Scholar · View at Zentralblatt MATH
  3. F. Li, “Asymptotic analysis of linearly viscoelastic shells–-justification of flexural shell equations,” Chinese Annals of Mathematics. Series A, vol. 28, no. 1, pp. 71–84, 2007. View at Google Scholar · View at Zentralblatt MATH
  4. F. Li, “Asymptotic analysis of linearly viscoelastic shells—justification of Koiter's shell equations,” Asymptotic Analysis, vol. 54, no. 1-2, pp. 51–70, 2007. View at Google Scholar · View at Zentralblatt MATH
  5. F. S. Li, “Convergence of the solution to general viscoelastic Koiter shell equations,” Acta Mathematica Sinica (English Series), vol. 23, no. 9, pp. 1683–1688, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. S. Li, “Global existence and uniqueness of weak solution to nonlinear viscoelastic full Marguerre-von Kármán shallow shell equations,” Acta Mathematica Sinica (English Series), vol. 25, no. 12, pp. 2133–2156, 2009. View at Publisher · View at Google Scholar
  7. F. Li and Y. Bai, “Uniform decay rates for nonlinear viscoelastic Marguerre-von Kármán equations,” Journal of Mathematical Analysis and Applications, vol. 351, no. 2, pp. 522–535, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. F. Li, “Limit behavior of the solution to nonlinear viscoelastic Marguerre-von Kármán shallow shell system,” Journal of Differential Equations, vol. 249, no. 6, pp. 1241–1257, 2010. View at Publisher · View at Google Scholar
  9. L.-M. Xiao, “Justification of two-dimensional nonlinear dynamic shell equations of Koiter's type,” Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 3, pp. 383–395, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. T. Li and T. Qin, Physics and Partial Differential Equations, vol. 2, Higher Educational Press, Beijing, China, 2000.
  11. G. Doetsch, Introduction to the Theory and Application of the Laplace Transformation, Springer, New York, NY, USA, 1974.