We consider a coefficient identification problem for a mathematical model with free boundary related to ductal carcinoma in situ (DCIS). This inverse problem aims to determine the nutrient consumption rate from additional measurement data at a boundary point. We first obtain a global‐in‐time uniqueness of our inverse problem. Then based on the optimization method, we present a regularization algorithm to recover the nutrient consumption rate. Finally, our numerical experiment shows the effectiveness of the proposed numerical method.

中文翻译：

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与导管癌相关的数学模型的系数识别问题

我们考虑与导管原位癌（DCIS）有关的具有自由边界的数学模型的系数识别问题。这个反问题旨在根据边界点的其他测量数据确定养分消耗率。我们首先获得逆问题的全局时间唯一性。然后基于优化方法，提出了一种恢复养分消耗率的正则化算法。最后，我们的数值实验表明了所提出数值方法的有效性。