Andrei Tarfulea (Louisiana State University)

Collective migration model on a viscoelastic collagen network.

We explore a model of self-generated directional cell migration on viscoelastic substrates in the absence of apparent intrinsic polarity. Mathematically, this takes the form of a reaction-diffusion equation for the network deformation, along with a moving cell-cluster source term which itself moves according to the local network deformation, leading to an unusual type of nonlinear interaction. We show global well-posedness, we find conditional existence/absence of traveling pulses (verifying a numerical observation by biologists), and we address the stability of these traveling pulses.