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Journal of Applied Mathematics
Volume 2015, Article ID 195460, 13 pages
http://dx.doi.org/10.1155/2015/195460
Research Article

Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

1School of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, China
2School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received 29 May 2015; Accepted 3 September 2015

Academic Editor: Carlos J. S. Alves

Copyright © 2015 Jun Guo 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. A. Henrot and M. Pierre, Variation et Optimisation de Formes: Une Analyse Géométrique, vol. 48 of Mathématiques et Applications, Springer, Berlin, Germany, 2005. View at Publisher · View at Google Scholar
  2. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, Germany, 2nd edition, 1998.
  3. L. Bourgeois, N. Chaulet, and H. Haddar, “Identication of generalized impedance boundary conditions: some numerical issues,” Tech. Rep. 7449, INRIA, 2010. View at Google Scholar
  4. J. Yang, B. Zhang, and H. Zhang, “Reconstruction of complex obstacles with generalized impedance boundary conditions from far-field data,” SIAM Journal on Applied Mathematics, vol. 74, no. 1, pp. 106–124, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. S. Jones, “Integral equations for the exterior acoustic problem,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 27, pp. 129–142, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. X. Liu and B. Zhang, “Direct and inverse obstacle scattering problems in a piecewise homogeneous medium,” SIAM Journal on Applied Mathematics, vol. 70, no. 8, pp. 3105–3120, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. X. Liu, B. Zhang, and G. Hu, “Uniqueness in the inverse scattering problem in a piecewise homogeneous medium,” Inverse Problems, vol. 26, no. 1, Article ID 015002, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. Kirsch and L. Päivärinta, “On recovering obstacles inside inhomogeneities,” Mathematical Methods in the Applied Sciences, vol. 21, no. 7, pp. 619–651, 1998. View at Google Scholar · View at MathSciNet · View at Scopus
  9. P. Hahner, “A uniqueness theorem for an inverse scattering problem in an exterior domain,” SIAM Journal on Mathematical Analysis, vol. 29, no. 5, pp. 1118–1128, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. I. Nachman, L. Päivärinta, and A. Teirilä, “On imaging obstacles inside inhomogeneous media,” Journal of Functional Analysis, vol. 252, no. 2, pp. 490–516, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. L. Bourgeois, N. Chaulet, and H. Haddar, “On simultaneous identification of the shape and generalized impedance boundary condition in obstacle scattering,” SIAM Journal on Scientific Computing, vol. 34, no. 3, pp. A1824–A1848, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Colton and A. Kirsch, “A simple method for solving inverse scattering problems in the resonance region,” Inverse Problems, vol. 12, no. 4, pp. 383–393, 1996. View at Publisher · View at Google Scholar · View at Scopus
  13. D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Problems, vol. 19, no. 6, pp. S105–S137, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Review, vol. 42, no. 3, pp. 369–414, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. F. Cakoni, M. di Cristo, and J. Sun, “A multistep reciprocity gap functional method for the inverse problem in a multilayered medium,” Complex Variables and Elliptic Equations, vol. 57, no. 2–4, pp. 261–276, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. D. Colton and H. Haddar, “An application of the reciprocity gap functional to inverse scattering theory,” Inverse Problems, vol. 21, no. 1, pp. 383–398, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. H. Zhang and B. Zhang, “A Newton method for a simultaneous reconstruction of an interface and a buried obstacle from far-field data,” Inverse Problems, vol. 29, no. 4, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. R. Kress, Acoustic Scattering: Special Theoretical Tools Scattering, edited by: R. Pike, P. Sabatier, Academic Press, London, UK, 2001.
  19. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Springer, Wiley, New York, NY, USA, 1983.
  20. W. McLean, Strongly Elliptic Systems and Boundary Integral Equation, Cambridge University Press, Cambridge, UK, 2000. View at MathSciNet
  21. F. Cakoni and R. Kress, “Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition,” Inverse Problems, vol. 29, no. 1, Article ID 015005, 19 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, USA, 1998.
  23. O. Bondarenko, A. Kirsch, and X. Liu, “The factorization method for inverse acoustic scattering in a layered medium,” Inverse Problems, vol. 29, no. 4, Article ID 045010, 19 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, vol. 36 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, UK, 2008. View at MathSciNet
  25. D. Colton, M. Piana, and R. Potthast, “A simple method using Morozov's discrepancy principle for solving inverse scattering problems,” Inverse Problems, vol. 13, no. 6, pp. 1477–1493, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus