粘弹性胶原网络上集体迁移的数学模型
Mathematical model for collective migration on a viscoelastic collagen network
AI总结：
本文为粘弹性基底上的自发集体迁移模型建立严格数学框架，证明高刚度下存在稳定行波脉冲及低刚度下稳态的指数收敛。
摘要：
本文研究在缺乏明显内在极性的情况下，细胞在粘弹性基底上自发定向迁移的模型。该模型首次在\cite{Clark}中提出，数值观察表明，当胶原刚度足够大时，模型表现出行波脉冲解，导致持续的集体迁移。本文为该模型提供了严格的数学框架，找到了精确的稳态和条件行波脉冲。我们还证明了在$W^{k,\infty}$空间中的全局适定性、高刚度下行波脉冲的局部稳定性，以及低刚度下向稳态的指数收敛。
英文摘要：
In this paper, we study a model of self-generated directional cell migration on viscoelastic substrates in the absence of apparent intrinsic polarity. This model, first proposed in \cite{Clark}, was observed numerically to manifest traveling pulse solutions for sufficiently large collagen stiffness, leading to a persistent collective migration. Here we provide a rigorous mathematical framework for the model, finding the exact stationary states and conditional traveling pulse. We also prove global well-posed in $W^{k,\infty}$ spaces, local stability of the traveling pulse for high stiffness, and exponential convergence to the stationary state for low stiffness.
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