中文摘要：

该文研究了一个热源识别问题，通过引入修正吉洪诺夫方法来处理问题的不适定性，在一种先验和一种后验参数选取准则下，分别获得了问题的误差估计．数值例子进一步验证了方法的有效性和稳定性．

英文摘要：

In this paper, we consider the problem for determining the unknown source in the heat equation. A modified Tikhonov regularization method is presented to deal with the illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable. Key words： Ill-posed problem; Unknown crepancy principle; Hilbert scales. source; Heat equation; Regularization method; Dis-