Dou, F.F., Fu, C.L. and Yang, F.L. (2009) Optimal Error Bound and Fourier Regularization for Identifying an Unknown Source in the Heat Equation. Journal of Computational and Applied Mathematics, 230, 728-737.
http://dx.doi.org/10.1016/j.cam.2009.01.008

has been cited by the following article:

• TITLE: The Tikhonov Regularization Method in Hilbert Scales for Determining the Unknown Source for the Modified Helmholtz Equation

  AUTHORS: Lei You, Zhi Li, Juang Huang, Aihua Du

  KEYWORDS: Ill-Posed Problem, Unknown Source, Regularization Method, Discrepancy Principle in Hilbert Scales

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.4 No.1, January 27, 2016

  ABSTRACT: In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.