标题： 具有过冷效应和表面张力的耦合不可压缩达西自由边界模型的行波存在性 显示英文标题

标题： Existence of traveling wave for a coupled incompressible Darcy's free boundary model with undercooling effect and surface tension

摘要： 在本文中，我们提出一个考虑细胞膜效应的细胞运动模型。该模型是一个不可压缩的达西自由边界问题。该模型在边界条件中包含一个非线性项，用于模拟膜的作用。该术语可以视为膜对细胞的过冷效应。它还意味着一个不稳定的非线性项在边界条件中，该非线性项依赖于极性标记物，并模拟细胞骨架的主动特性。首先，我们研究了稳态的线性稳定性，并证明在阈值以上，圆盘是线性不稳定的。这一分析突出了过冷的稳定效应。然后，使用分岔论证，我们证明了描述细胞迁移持续运动的行波的存在，并验证了该模型的相关性。 显示英文摘要

摘要： In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model the action of the membrane. This term can be seen as a undercooling effect of the membrane on the cell. It also implies a destabilizing nonlinear term in the boundary condition, depending on polarity markers and modeling the active character of the cytoskeleton. First, we study the linear stability of the steady state and prove that above a threshold, the disk is linearly unstable. This analysis highlights the stabilizing effect of undercooling. Then, using a bifurcation argument, we prove the existence of traveling waves that describe a persistent motion in cell migration and justify the relevance of the model.