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Mathematical Problems in Engineering
Volume 2006, Article ID 49797, 12 pages
http://dx.doi.org/10.1155/MPE/2006/49797

Reconstruction of round voids in the elastic half-space: Antiplane problem

1Faculty of Mechanics and Mathematics, Rostov State University, 5 Zorge Street, Rostov-on-Don 344090, Russia
2Dipartimento di Ingegneria dell' Informazione e Matematica Applicata, University of Salerno, Via Ponte don Melillo, Fisciano (SA) 84084, Italy

Received 15 February 2005; Revised 24 May 2005; Accepted 12 July 2005

Copyright © 2006 Mezhlum A. Sumbatyan et al. 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. G. Alessandrini, E. Beretta, and S. Vessella, “Determining linear cracks by boundary measurements: Lipschitz stability,” SIAM J. Math. Anal., vol. 27, no. 2, pp. 361–375, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Andrieux and A. Ben Abda, “Identification of planar cracks by complete overdetermined data: inversion formulae,” Inverse Problems, vol. 12, no. 5, pp. 553–563, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Bannour, A. Ben Abda, and M. Jaoua, “A semi-explicit algorithm for the reconstruction of 3D planar cracks,” Inverse Problems, vol. 13, no. 4, pp. 899–917, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. R. Barber, Elasticity, vol. 107 of Solid Mechanics and Its Applications, Kluwer Academic, Dordrecht, 2nd edition, 2002. View at MathSciNet
  5. A. Ben Abda, M. Kallel, J. Leblond, and J.-P. Marmorat, “Line segment crack recovery from incomplete boundary data,” Inverse Problems, vol. 18, no. 4, pp. 1057–1077, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Bonnet, Boundary Integral Equations Methods for Solids and Fluids, John Wiley & Sons, New York, 1999.
  7. A. Corana, M. Marchesi, C. Martini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm,” ACM Trans. Math. Software, vol. 13, no. 3, pp. 262–280, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Friedman and M. Vogelius, “Determining cracks by boundary measurements,” Indiana Univ. Math. J., vol. 38, no. 3, pp. 527–556, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, Academic Press, London, 1981. View at Zentralblatt MATH · View at MathSciNet
  10. O. D. Kellogg, Foundations of Potential Theory, Dover, New York, 1953. View at Zentralblatt MATH
  11. M. A. Sumbatyan and A. Scalia, Equations of Mathematical Diffraction Theory, vol. 5 of Differential and Integral Equations and Their Applications, Chapman & Hall/CRC, Florida, 2005. View at Zentralblatt MATH · View at MathSciNet