Collective motion driven by nutrient consumption
Abstract
A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary Differential Equation system which we scale so as to get a limit describing the usually observed pattern. In this limit the cell density is concentrated as a moving Dirac mass and the nutrient undergoes a discontinuity. We first carry out the analysis without diffusion, getting a complete description of the unique limit. When diffusion is included, we prove several specific a priori estimates and interpret the system as a heterogeneous monostable equation. This allow us to obtain a limiting problem which shows the concentration effect of the limiting dynamics.
Cite
@article{arxiv.2209.00100,
title = {Collective motion driven by nutrient consumption},
author = {Pierre-Emmanuel Jabin and Benoît Perthame},
journal= {arXiv preprint arXiv:2209.00100},
year = {2022}
}