Propagating Profiles of a Chemotaxis Model with Degenerate Diffusion: Initial Shrinking, Eventual Smoothness and Expanding

TL;DR

This paper studies a chemotaxis model with degenerate diffusion, revealing how initial conditions influence bacterial clustering, support shrinking, and spreading speed, with implications for understanding bacterial behavior.

Contribution

It provides new insights into the effects of initial attractant distribution on bacterial clustering and derives explicit formulas for spreading speed in a chemotaxis model.

Findings

Support may shrink under certain attractant conditions

Finite speed of propagation is established without special attractant assumptions

Explicit formula for spreading speed in terms of model parameters

Abstract

We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect of the initial attractant distribution on bacterial clustering. We prove that the compact support of solutions may shrink if the signal concentration satisfies a special structure, and show the finite speed propagating property without assuming the special structure on attractant concentration, and obtain an explicit formula of the population spreading speed in terms of model parameters. The presented results suggest that bacterial cluster formation can be affected by chemotactic attractants and density-dependent dispersal.