ABSTRACT In this paper, we consider the source strength identification problem for the three-dimensional inverse heat conduction equations. The problem is to determine an unknown heat source strength from the measurement data for a specified location. In this process, the direct problem is solved by applying the Green’s function method. Then, this problem can be converted into a Volterra integral equation of the first kind. Further, the Tikhonov and truncated singular value decomposition regularization methods are developed to identify the unknown source strength based on the discrepancy principle for choosing the regularization parameter. Finally, numerical examples are presented to show the feasibility and efficiency of the proposed method.

中文翻译：

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三维逆导热方程的源强度识别问题

摘要 在本文中，我们考虑了三维逆热传导方程的源强度识别问题。问题是根据指定位置的测量数据确定未知的热源强度。在这个过程中，直接问题是通过应用格林函数方法解决的。那么，这个问题就可以转化为第一类沃尔泰拉积分方程。此外，基于选择正则化参数的差异原则，开发了 Tikhonov 和截断奇异值分解正则化方法来识别未知源强度。最后，通过数值例子说明了所提出方法的可行性和有效性。