In this paper, we consider the inverse source problem of heat conduction equation with time-dependent diffusivity on a spherical symmetric domain. This problem is ill-posed, i.e. the solution of the problem does not depend continuously on the measured data. To solve this problem, we propose an iterative regularization method and obtain the Hölder type error estimates. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

中文翻译：

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球对称域上扩散系数随时间变化的热传导方程的逆源问题

在本文中，我们考虑球对称域上具有瞬态扩散率的热传导方程的逆源问题。这个问题是不适定的，即问题的解决方案不连续依赖于测量数据。为了解决这个问题，我们提出了一种迭代正则化方法并获得了 Hölder 类型的误差估计。给出了数值例子来证明所提出方法的有效性。