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 Wk,∞ spaces, local stability of the traveling pulse for high stiffness, and exponential convergence to the stationary state for low stiffness.
@article{arxiv.2501.13892,
title = {Mathematical model for collective migration on a viscoelastic collagen network},
author = {Nicolas Meunier and Andrei Tarfulea},
journal= {arXiv preprint arXiv:2501.13892},
year = {2025}
}