We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. The model features two moving interfaces separating the tumor, the normal tissue, and the exterior vacuum. We prove local-in-time existence and uniqueness of strong solutions for their evolution starting from a nearly radial initial configuration. It is assumed that the tumor has lower mobility than the normal tissue, which is in line with the well-known Saffman–Taylor condition in viscous fingering.

中文翻译：

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两相肿瘤生长模型中的界面动力学

我们在两个空间维度研究肿瘤生长模型，其中肿瘤细胞的增殖导致肿瘤域的扩张和周围正常组织迁移到外部真空中。该模型具有分隔肿瘤、正常组织和外部真空的两个移动界面。我们证明了强解的局部时间存在性和唯一性，它们从近乎径向的初始配置开始演化。假设肿瘤的活动性低于正常组织，这符合粘性指法中众所周知的 Saffman-Taylor 条件。