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J. R. Cannon and P. Du Chateau, “Structural Identification of an Unknown Source term in a Heat Equation,” Inverse Problems, Vol. 14, No. 3, 1998, pp. 535-551. http://dx.doi.org/10.1088/0266-5611/14/3/010

has been cited by the following article:

• TITLE: Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales

  AUTHORS: Zhenyu Zhao, Ou Xie, Zehong Meng, Lei You

  KEYWORDS: Ill-Posed Problem; Unknown Source; Heat Equation; Regularization Method; Discrepancy Principle in Hilbert Scales

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.2, January 17, 2014

  ABSTRACT: In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choice rule. Numerical tests show that the proposed method is effective and stable.