论文标题
没有单调性的Hele-Shaw限制
A Hele-Shaw limit without monotonicity
论文作者
论文摘要
我们研究了代表源或水槽项的右侧多孔培养基方程的不可压缩极限，以及注入边界条件。该模型可以看作是对肿瘤生长和人群运动中非主持酮运动的简化描述，从而推广了最近文献中仅交通拥堵的动作（\ cite {aky}，\ cite {pqv}，\ cite {kp}，\ cite {kp}，\ cite {mpq}）。我们表征了极限密度，该密度在极限压力方面解决了Hele-Shaw类型的自由边界问题。我们结果的新颖特征在于极限压力的表征，这在进化中每次都解决了障碍问题
We study the incompressible limit of the porous medium equation with a right hand side representing either a source or a sink term, and an injection boundary condition. This model can be seen as a simplified description of non-monotone motions in tumor growth and crowd motion, generalizing the congestion-only motions studied in recent literature (\cite{AKY}, \cite{PQV}, \cite{KP}, \cite{MPQ}). We characterize the limit density, which solves a free boundary problem of Hele-Shaw type in terms of the limit pressure. The novel feature of our result lies in the characterization of the limit pressure, which solves an obstacle problem at each time in the evolution
