This paper is devoted to numerical analysis of an inverse source problem in a degenerate parabolic equation. The aims of this work are to show the well-posedness of the discrete inverse problem and its convergence to the continuous one. For this, we reformulate first the encountered inverse problem to a regularized optimal control one. Then, we approximate our optimal control problem by finite element method and we show the existence of the discrete solution and its convergence to the continuous one. Finally, in order to confirm the efficiency of the proposed scheme, some numerical results are obtained using the augmented Lagrangian method.

中文翻译：

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内退化抛物方程反源问题的数值研究

本文致力于对退化抛物方程中的逆源问题进行数值分析。这项工作的目的是展示离散逆问题的适定性及其对连续逆问题的收敛性。为此，我们首先将遇到的逆问题重新表述为正则化最优控制问题。然后，我们用有限元方法逼近我们的最优控制问题，并证明了离散解的存在及其对连续解的收敛性。最后，为了确认所提出方案的有效性，使用增广拉格朗日方法获得了一些数值结果。