Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption
Abstract
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The former induces a chemotactic bias in the diffusive motion of the cells and is accounted for by a density-suppressed motility. Well-posedness is first established for generic positive and non-increasing motility functions vanishing at infinity. Growth conditions on the motility function guaranteeing the uniform-in-time boundedness of solutions are next identified. Finally, for sublinearly decaying motility functions, convergence to a spatially homogeneous steady state is shown, with an exponential rate for consumption rates behaving linearly near zero.
Keywords
Cite
@article{arxiv.2106.02368,
title = {Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption},
author = {Jie Jiang and Philippe Laurençot and Yanyan Zhang},
journal= {arXiv preprint arXiv:2106.02368},
year = {2021}
}