We consider a nonlinear free boundary system for the nutrient concentration, which comes from the mathematical model of ductal carcinoma in situ (DCIS). The motion of the free boundary is given by an integro-differential equation. The existence and uniqueness of the incomplete radial solution for a finite time interval is established, and a novel effective numerical method for simulating the growth of tumor is developed. Results are supported by numerical experiments.

中文翻译：

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导管癌原位模拟的自由边界问题的存在与数值方法

我们考虑营养物浓度的非线性自由边界系统，该系统来自导管原位癌（DCIS）的数学模型。自由边界的运动由积分微分方程给出。建立了有限时间间隔内不完全径向解的存在性和唯一性，并开发了一种新型的模拟肿瘤生长的有效数值方法。结果得到数值实验的支持。