In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of nutrients, oxygen, or, possibly, as a result of self-propulsion. The main result of this work is the incompressible limit of this model which builds a bridge between the density-based model and a geometry free-boundary problem by passing to a singular limit in the pressure law. The limiting objects are then proven to be unique.

中文翻译：

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考虑对流效应的肿瘤生长模型的不可压缩极限

在这项工作中，我们研究了一种应用于肿瘤生长的组织生长模型。该模型基于 Perthame、Quirós 和 Vázquez 在 2014 年提出的模型，但纳入了对流效应，例如由于营养物、氧气的存在，或者可能是由于自推进而引起的。这项工作的主要结果是该模型的不可压缩极限，它通过传递到压力定律中的奇异极限，在基于密度的模型和几何自由边界问题之间架起了一座桥梁。然后证明限制对象是唯一的。