论文标题
密度约束的趋化性和Hele-shaw流动
Density-constrained Chemotaxis and Hele-Shaw flow
论文作者
论文摘要
我们考虑了趋化性的拥塞动力学模型，其中细胞的密度遵循其产生的化学信号，同时观察到不可压缩性约束。我们表明，当化学物质缓慢扩散并强烈吸引细胞时，充血细胞的动力学通过表面张力驱动的自由边界问题很好地近似。更确切地说，我们表明，在此限制中，细胞的密度收敛到集合的特征函数，该集合的演变由Hele-Shaw自由边界问题与表面张力描述。我们的问题设置在一个有限的域中，这导致了对密度函数的限制边界条件的有趣分析。也就是说，我们证明了化学势的罗宾边界条件的假设会导致自由界面的接触角条件。
We consider a model of congestion dynamics with chemotaxis, where the density of cells follows the chemical signal it generates, while observing an incompressibility constraint. We show that when the chemical diffuses slowly and attracts the cells strongly, then the dynamics of the congested cells is well approximated by a surface-tension driven free boundary problem. More precisely, we show that in this limit the density of cell converges to the characteristic function of a set whose evolution is described by a Hele-Shaw free boundary problem with surface tension. Our problem is set in a bounded domain, which leads to an interesting analysis on the limiting boundary conditions for the density function. Namely, we prove that the assumption of Robin boundary conditions for the chemical potential leads to a contact angle condition for the free interface.
