Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 598135, 6 pages
http://dx.doi.org/10.1155/2014/598135
Research Article

Conditional Stability for an Inverse Problem of Determining a Space-Dependent Source Coefficient in the Advection-Dispersion Equation with Robin’s Boundary Condition

1College of Mathematics and Statistics, Nanyang Normal University, Nanyang, Henan 473061, China
2Institute of Applied Mathematics, Shandong University of Technology, Zibo, Shandong 255049, China

Received 3 December 2013; Revised 27 February 2014; Accepted 27 February 2014; Published 24 April 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Shunqin Wang 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. P. DuChateau, “Monotonicity and invertibility of coefficient-to-data mappings for parabolic inverse problems,” SIAM Journal on Mathematical Analysis, vol. 26, no. 6, pp. 1473–1487, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. DuChateau, “An inverse problem for the hydraulic properties of porous media,” SIAM Journal on Mathematical Analysis, vol. 28, no. 3, pp. 611–632, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. DuChateau, “An adjoint method for proving identifiability of coefficients in parabolic equations,” Journal of Inverse and Ill-Posed Problems, vol. 21, no. 5, pp. 639–663, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Hasanov, P. DuChateau, and B. Pektaş, “An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation,” Journal of Inverse and Ill-Posed Problems, vol. 14, no. 5, pp. 435–463, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. H. Ou, A. Hasanov, and Z. H. Liu, “Inverse coefficient problems for nonlinear parabolic differential equations,” Acta Mathematica Sinica, vol. 24, no. 10, pp. 1617–1624, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Li, D. Yao, and F. Yang, “An inverse problem of identifying source coefficient in solute transportation,” Journal of Inverse and Ill-Posed Problems, vol. 16, no. 1, pp. 51–63, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. N.-Z. Sun, Mathematical Modeling of Groundwater Pollution, Springer, New York, NY, USA, 1996. View at MathSciNet
  8. J. R. Cannon, The One-Dimensional Heat Equation, vol. 23, Addison-Wesley, London, UK, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  9. I. Bushuyev, “Global uniqueness for inverse parabolic problems with final observation,” Inverse Problems, vol. 11, no. 4, pp. L11–L16, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Choulli and M. Yamamoto, “Conditional stability in determining a heat source,” Journal of Inverse and Ill-Posed Problems, vol. 12, no. 3, pp. 233–243, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. V. Isakov, “Some inverse problems for the diffusion equation,” Inverse Problems, vol. 15, no. 1, pp. 3–10, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. E. G. Savateev and R. Riganti, “Inverse problem for the nonlinear heat equation with the final overdetermination,” Mathematical and Computer Modelling, vol. 22, no. 1, pp. 29–43, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. R. Cannon and P. DuChateau, “Structural identification of an unknown source term in a heat equation,” Inverse Problems, vol. 14, no. 3, pp. 535–551, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. Li, “Data compatibility and conditional stability for an inverse source problem in the heat equation,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 566–581, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. P. Sperb, Maximum Principles and Their Applications, vol. 157, Academic Press, New York, NY, USA, 1981. View at MathSciNet
  16. R. Courant and D. Hilbert, Methods of Mathematical Physics I, Interscience, New York, NY, USA, 1953. View at MathSciNet
  17. L. Gongsheng and M. Yamamoto, “Stability analysis for determining a source term in a 1-D advection-dispersion equation,” Journal of Inverse and Ill-Posed Problems, vol. 14, no. 2, pp. 147–155, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet