Traveling waves and their spectral instability in volume-filling chemotaxis model

In this paper, I consider a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By the geometric singular perturbation theory together with the center-stable and center unstable manifolds, one gets the existence of a positive traveling wave connecting the two constant steady states (0, 0) and (b, alpha beta/beta) with a small wave speed epsilon c. In addition, the traveling wave is monotone for b >= 1 and is not monotone for 0 < b < 1. Moreover, by the spectral analysis it shows that the above traveling wave is spectrally unstable in some exponentially weighted spaces.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By using the geometric singular perturbation theory, the existence of a positive traveling wave connecting two constant steady states is confirmed. The monotonicity of the wave is analyzed for different parameter ranges, and spectral instability is observed in some exponentially weighted spaces.