考虑过冷效应和表面张力的耦合不可压缩 Darcy 自由边界模型的行波存在性
Existence of traveling wave for a coupled incompressible Darcy's free boundary model with undercooling effect and surface tension
AI总结：
本文建立含膜过冷效应与细胞骨架主动失稳项的不可压缩 Darcy 自由边界细胞运动模型，分析圆盘稳态稳定性并通过分岔证明持续迁移行波存在。
摘要：
本文提出了一个考虑细胞膜效应的细胞运动模型。所引入的模型是一个不可压缩 Darcy 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。这一项可视为膜对细胞的过冷效应。它还意味着边界条件中存在一个失稳非线性项，该项取决于极性标记，并模拟细胞骨架的主动特性。首先，我们研究稳态的线性稳定性，并证明在超过某个阈值后，圆盘呈线性不稳定。该分析突出了过冷的稳定作用。随后，利用分岔论证，我们证明了描述细胞迁移中持续运动的行波的存在性，并论证了该模型的相关性。
英文摘要：
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.
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