Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2016 (2016), Article ID 9504829, 5 pages
http://dx.doi.org/10.1155/2016/9504829
Research Article

A Lipschitz Stability Estimate for the Inverse Source Problem and the Numerical Scheme

Shandong University of Technology, Shandong 255000, China

Received 4 May 2016; Accepted 27 June 2016

Academic Editor: Soheil Salahshour

Copyright © 2016 Xianzheng Jia. 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. 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 MathSciNet · View at Scopus
  2. L. Yan, C.-L. Fu, and F.-L. Yang, “The method of fundamental solutions for the inverse heat source problem,” Engineering Analysis with Boundary Elements, vol. 32, no. 3, pp. 216–222, 2008. View at Google Scholar
  3. S. Chantasiriwan, “Methods of fundamental solutions for time-dependent heat conduction problems,” International Journal for Numerical Methods in Engineering, vol. 66, no. 1, pp. 147–165, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Yan, F.-L. Yang, and C.-L. Fu, “A meshless method for solving an inverse spacewise-dependent heat source problem,” Journal of Computational Physics, vol. 228, no. 1, pp. 123–136, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. N. Ahmadabadi, M. Arab, and F. M. M. Ghaini, “The method of fundamental solutions for the inverse space-dependent heat source problem,” Engineering Analysis with Boundary Elements, vol. 33, no. 10, pp. 1231–1235, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. T. Johansson and D. Lesnic, “Determination of a spacewise dependent heat source,” Journal of Computational and Applied Mathematics, vol. 209, no. 1, pp. 66–80, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. A. Farcas and D. Lesnic, “The boundary-element method for the determination of a heat source dependent on one variable,” Journal of Engineering Mathematics, vol. 54, no. 4, pp. 375–388, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. B. T. Johansson and D. Lesnic, “A variational method for identifying a spacewise-dependent heat source,” IMA Journal of Applied Mathematics, vol. 72, no. 6, pp. 748–760, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. B. T. Johansson and D. Lesnic, “A procedure for determining a spacewise dependent heat source and the initial temperature,” Applicable Analysis, vol. 87, no. 3, pp. 265–276, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  10. B. Jin and L. Marin, “The method of fundamental solutions for inverse source problems associated with the steady-state heat conduction,” International Journal for Numerical Methods in Engineering, vol. 69, no. 8, pp. 1570–1589, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. F. Wang, W. Chen, and L. Ling, “Combinations of the method of fundamental solutions for general inverse source identification problems,” Applied Mathematics and Computation, vol. 219, no. 3, pp. 1173–1182, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. M. Mierzwiczak and J. A. Kolodziej, “Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem,” Computer Physics Communications, vol. 181, no. 12, pp. 2035–2043, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Mierzwiczak and J. A. Kołodziej, “Application of the method of fundamental solutions with the Laplace transformation for the inverse transient heat source problem,” Journal of Theoretical and Applied Mechanics, vol. 50, no. 4, pp. 1011–1023, 2012. View at Google Scholar · View at Scopus
  14. E. G. Savateev, “On problems of determining the source function in a parabolic equation,” Journal of Inverse and Ill-Posed Problems, vol. 3, no. 1, pp. 83–102, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. D. Trong, N. T. Long, and P. N. Alain, “Nonhomogeneous heat equation: identification and regularization for the inhomogeneous term,” Journal of Mathematical Analysis and Applications, vol. 312, no. 1, pp. 93–104, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. A. Shidfar, B. Jazbi, and M. Alinejadmofrad, “Inverse estimation of the pulse parameters of a time-varying laser pulse to obtain desired temperature at the material surface,” Optics and Laser Technology, vol. 44, no. 6, pp. 1675–1680, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Saitoh, V. K. Tuan, and M. Yamamoto, “Reverse convolution inequalities and applications to inverse heat source problems,” Journal of Inequalities in Pure and Applied Mathematics, vol. 3, no. 5, article 80, 2002. View at Google Scholar · View at MathSciNet
  18. S. Itô, Diffusion Equations, AMS, Providence, RI, USA, 1992. View at MathSciNet