2025/01/23 by Nicolas Meunier, Meunier, Nicolas, Andrei Tarfulea +1
Materials Science · #Collagen: Extraction and Characterization
paper · pdf · doi:10.48550/arxiv.2501.13892
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 \citeClark, 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.