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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 891078, 11 pages
http://dx.doi.org/10.1155/2012/891078
Research Article

The Inverse Problem for a General Class of Multidimensional Hyperbolic Equations

1Department of Economics and CRED, University of Namur (FUNDP), 5000 Namur, Belgium
2ECARES, Université libre de Bruxelles, 1050 Bruxelles, Belgium
3Department of Mathematics, Aktobe State University, 030000 Aktobe, Kazakhstan

Received 1 July 2011; Accepted 4 August 2011

Academic Editor: Carlo Cattani

Copyright © 2012 Gani Aldashev and Serik A. Aldashev. 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. M. Lavrentiev, V. Romanov, and V. Vasiliev, Multidimensional Inverse Problems for Differential Equations, Springer, New York, NY, USA, 1970.
  2. V. Romanov, Some Inverse Problems for the Equations of Hyperbolic Type, Nauka, Novosibirsk, Russia, 1972.
  3. V. Isakov, Inverse Problems for Partial Differential Equations, Springer, New York, NY, USA, 2006. View at Zentralblatt MATH
  4. S. Y. Chen, Y. F. Li, Q. Guan, and G. Xiao, “Real-time three-dimensional surface measurement by color encoded light projection,” Applied Physics Letters, vol. 89, no. 11, Article ID 111108, 2006. View at Publisher · View at Google Scholar
  5. S. Y. Chen, H. Tong, and C. Cattani, “Markov models for image labeling,” Mathematical Problems in Engineering, vol. 2011, Article ID 814356, 18 pages, 2011. View at Publisher · View at Google Scholar
  6. S. Y. Chen and Q. Guan, “Parametric shape representation by a deformable NURBS model for cardiac functional measurements,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 3, pp. 480–487, 2011. View at Publisher · View at Google Scholar · View at PubMed
  7. R. Engbers, M. Burger, and V. Capasso, Inverse Problems in Geographical Economics: Parameter Identification in the Spatial Solow Model, University of Muenster, Muenster, Germany, 2011.
  8. M. Carrasco, J.-P. Florens, and E. Renault, “Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization,” in Handbook of Econometrics, J. Heckman and E. Leamer, Eds., vol. 7, chapter 77, pp. 5633–5751, North-Holland, Amsterdam, The Netherlands, 2007.
  9. C. A. Favero and R. Rovelli, “Macroeconomic stability and the preferences of the Fed: a formal analysis, 1961-98,” Journal of Money, Credit and Banking, vol. 35, no. 4, pp. 545–556, 2003.
  10. E. Castelnuovo and P. Surico, “Model uncertainty, optimal monetary policy and the preferences of the fed,” Scottish Journal of Political Economy, vol. 51, no. 1, pp. 105–126, 2004. View at Publisher · View at Google Scholar
  11. P. Brito, The Dynamics of Growth and Distribution in a Spatially Heterogeneous World. Working Paper, ISEG, Technical University of Lisbon, Lisbon, Portugal, 2004.
  12. R. Boucekkine, C. Camacho, and B. Zou, “Bridging the gap between growth theory and the new economic geography: the spatial Ramsey model,” Macroeconomic Dynamics, vol. 13, no. 1, pp. 20–45, 2009. View at Publisher · View at Google Scholar
  13. J.-P. Puel and M. Yamamoto, “Generic well-posedness in a multidimensional hyperbolic inverse problem,” Journal of Inverse and Ill-Posed Problems, vol. 5, no. 1, pp. 55–83, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. G. Ramm and Rakesh, “Property C and an inverse problem for a hyperbolic equation,” Journal of Mathematical Analysis and Applications, vol. 156, no. 1, pp. 209–219, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. Daveau, D. Douady, and A Khelifi, “On a hyperbolic coefficient inverse problem via partial dynamic boundary measurements,” Journal of Applied Mathematics, Article ID 561395, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations, Pergamon, New York, NY, USA, 1965.
  17. V. Smirnov, A Course in Higher Mathematics, vol. 4, part 2, Addison-Wesley, Boston, Mass, USA, 1964.
  18. S. Aldashev, Boundary-Value Problems for Multi-Dimensional Hyperbolic and Mixed Equations, Gylym Press, Almaty, Kazakhstan, 1994.
  19. S. A. Aldashev, “On Darboux problems for a class of multidimensional hyperbolic equations,” Differentsialnye Uravneniya, vol. 34, no. 1, pp. 64–68, 1998.
  20. A. V. Bitsadze, Equations of the Mixed Type, Pergamon, New York, NY, USA, 1964.
  21. E. T. Copson, “On the Riemann-Green function,” Archive for Rational Mechanics and Analysis, vol. 1, pp. 324–348, 1958. View at Zentralblatt MATH
  22. A. Nakhushev, The Equations of Mathematical Biology, Nauka Press, Moscow, Russia, 1995.
  23. H. Bateman and A. Erdelyi, Higher Transcendental Functions, vol. 1, McGraw–Hill, New York, NY, USA, 1955.
  24. L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon, New York, NY, USA, 2nd edition, 1982.
  25. A. Kolmogorov and S. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover Publications, Mineola, NY, USA, 1999.