A mathematical model for tissue growth is considered. This model describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that such cell population model converges at the incompressible limit towards a Hele-Shaw type free boundary problem. The novelty of this work is to impose a non-overlapping constraint. This constraint is important to be satisfied in many applications. One way to guarantee this non-overlapping constraint is to choose a singular pressure law. The aim of this paper is to prove that, although the pressure law has a singularity, the incompressible limit leads to the same Hele-Shaw free boundary problem.

中文翻译：

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具有非重叠约束的组织生长力学模型的不可压缩极限

考虑组织生长的数学模型。该模型描述了由于压力和增殖引起的细胞密度动态。众所周知，这种细胞群模型在不可压缩极限处收敛于 Hele-Shaw 型自由边界问题。这项工作的新颖之处在于施加了非重叠约束。在许多应用中满足这个约束很重要。保证这种非重叠约束的一种方法是选择奇异压力定律。本文的目的是证明，尽管压力定律具有奇异性，但不可压缩极限会导致相同的 Hele-Shaw 自由边界问题。