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.
Xiao-Xiao Li. Heng Zhen Guo. Shi Min Wan. Fan Yang. "Inverse Source Identification by the Modified Regularization Method on Poisson Equation." J. Appl. Math. 2012 1 - 13, 2012. https://doi.org/10.1155/2012/971952