Mathematical model for collective migration on a viscoelastic collagen network
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 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.
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