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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 320456, 6 pages
An Interior Inverse Problem for the Diffusion Operator
1Islamic Azad University, Neka Branch, P.O. Box 48411-86114, Neka, Iran
2Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
3Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran
Received 27 April 2013; Accepted 4 June 2013
Academic Editor: Dumitru Baleanu
Copyright © 2013 A. Dabbaghian 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.
- K. Aki and P. G. Richards, in Quantitative Seismology: Theory and Methods, vol. 1, chapter 8, pp. 337–381, W. H. Freeman, New York, NY, USA, 1980.
- W. Rundell and P. E. Sacks, “Reconstruction of a radially symmetric potential from two spectral sequences,” Journal of Mathematical Analysis and Applications, vol. 264, no. 2, pp. 354–381, 1991.
- H. P. Baltes, Inverse Scattering Problems in Optics, vol. 20 of Topics in Current Physics, Springer, Berlin, Germany, 1980.
- L. Hogben, “Spectral graph theory and inverse eigenvalue problem of a graph,” Chamchuri Journal of Mathematics, vol. 1, no. 1, pp. 51–72, 2009.
- C. R. Johnson, A. Leal-Duarte, and C. M. Saiago, “Inverse eigenvalue problems and lists of multiplicities of eigengvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars,” Linear Algebra and Its Applications, vol. 373, pp. 311–330, 2003.
- R. L. Parker and K. A. Whaler, “Numerical methods for establishing solutions to theinverse problem of electromagnetic induction,” Journal of Geophysical Research, vol. 86, no. 10, pp. 9574–9584, 1981.
- V. Yurko, “Uniqueness of recovering differential operators on hedgehog-type graphs,” Advances in Dynamical Systems and Applications, vol. 4, no. 2, pp. 231–241, 2009.
- G. Freiling and V. A. Yurko, Inverse Sturm-Liouville Problems and Their Applications, Nova Science, New York, NY, USA, 2001.
- O. H. Hald, “Discontinuous inverse eigenvalue problems,” Communications on Pure and Applied Mathematics, vol. 37, no. 5, pp. 539–577, 1984.
- O. N. Livinenko and V. I. Soshnikov, The Theory of Heterogeneous Lines and Their Applications in Radio Engineering, Radio, Moscow, Russia, 1964 (Russian).
- J. R. McLaughlin and P. L. Polyakov, “On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues,” Journal of Differential Equations, vol. 107, no. 2, pp. 351–382, 1994.
- V. P. Meschanov and A. L. Feldstein, Automatic Design of Directional Couplers, Sviaz, Moscow, Russia, 1980.
- R. S. Anderssen, “The effect of discontinuities in density and shear velocity onthe asymptotic overtone structure of torsional eigenfrequencies of the Earth,” Geophysical Journal of the Royal Astronomical Society, vol. 50, pp. 303–309, 1997.
- F. R. Lapwood and T. Usami, Free Oscillations of the Earth, Cambridge University Press, Cambridge, UK, 1981.
- G. Freiling and V. A. Yurko, “Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point,” Inverse Problems, vol. 18, no. 3, pp. 757–773, 2002.
- R. J. Krueger, “Inverse problems for nonabsorbing media with discontinuous material properties,” Journal of Mathematical Physics, vol. 23, no. 3, pp. 396–404, 1982.
- V. A. Yurko, “On boundary value problems with discontinuity conditions inside an interval,” Differentsial'nye Uravneniya, vol. 36, no. 8, pp. 1139–1140, 2000 (Russian), English Translation in Differential Equations, vol. 8, no. 8, pp. 1266–1269, 2000.
- K. Mochizuki and I. Trooshin, “Inverse problem for interior spectral data of the Sturm-Liouville operator,” Journal of Inverse and Ill-Posed Problems, vol. 9, no. 4, pp. 425–433, 2001.
- K. Mochizuki and I. Trooshin, “Inverse problem for interior spectral data of the Dirac operator on a finite interval,” Publicationsof the Research Institute for Mathematical Sciences, Kyoto University, vol. 38, no. 2, pp. 387–395, 2002.
- C. F. Yang and X. P. Yang, “An interior inverse problem for the Sturm-Liouville operator with discontinuous conditions,” Applied Mathematics Letters, vol. 22, no. 9, pp. 1315–1319, 2009.
- M. G. Gasymov and G. Š. Guseĭnov, “Determination of a diffusion operator from spectral data,” Akademiya Nauk Azerbaĭdzhanskoĭ SSR. Doklady, vol. 37, no. 2, pp. 19–23, 1981.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional calculus: models and numerical methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, Mass, USA, 2012.
- X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
- X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, China, 2011.