论文标题
耦合不可压缩的达西的自由边界问题的行驶波解决方案与表面张力
Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension
论文作者
论文摘要
我们研究了最近在[22]中引入的不可压缩的达西的自由边界问题。我们的目标是证明存在非平凡的行驶波解决方案，从而验证该模型描述细胞运动的兴趣。模型方程包括极性标记浓度的对流扩散方程和不可压缩的Darcy方程。这个问题的数学新颖性是在描述细胞细胞骨架的活动特征的边界条件下的非线性不稳定项。我们首先研究了该问题的线性稳定性，我们表明，在精确的阈值之上，磁盘变得线性不稳定。通过使用两种不同的方法，我们证明了波动波解的存在，它描述了生物细胞的持续运动。一个是通过施工明确的。另一个是隐式建立的，是一个从固定溶液中分叉的。
We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate the interest of this model to describe cell motility. The model equations include a convection diffusion equation for the polarity marker concentration and the incompressible Darcy's equation. The mathematical novelty of this problem is the nonlinear destabilizing term in the boundary condition that describes the active character of the cell cytoskeleton. We first study the linear stability of this problem and we show that, above a well precise threshold, the disk becomes linearly unstable. By using two different approaches we prove existence of traveling wave solutions, which describes persistent motion of a biological cell. One is explicit, by construction. The other is established implicitly, as the one bifurcating from stationary solution.
