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Journal of Applied Mathematics
Volume 2012, Article ID 971952, 13 pages
http://dx.doi.org/10.1155/2012/971952
Research Article

Inverse Source Identification by the Modified Regularization Method on Poisson Equation

1School of Science, Lanzhou University of Technology, Lanzhou 730050, China
2Institute of Education, Lanzhou City University, Lanzhou 730070, China
3Department of Fundamental Subject, Tianjin Institute of Urban Construction, Tianjin 300384, China

Received 23 June 2011; Revised 21 September 2011; Accepted 10 October 2011

Academic Editor: Nicola Guglielmi

Copyright © 2012 Xiao-Xiao Li 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.

Abstract

This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization solution and the exact solution. The numerical results show that the proposed method is stable and the unknown source is recovered very well.