Mathematical model for collective migration on a viscoelastic collagen network

Nicolas Meunier; Andrei Tarfulea

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arXiv · 2501.13892

Mathematical model for collective migration on a viscoelastic collagen network

Nicolas Meunier·Andrei Tarfulea

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Abstract

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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Nicolas Meunier, Andrei Tarfulea. 2025-01-23. Mathematical model for collective migration on a viscoelastic collagen network. https://arxiv.org/abs/2501.13892

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