No pattern formation in a quasilinear chemotaxis model with local sensing

2024/04/18 by Laurençot, Philippe, Trescases, Ariane
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.12166

Abstract

Convergence to spatially homogeneous steady states is shown for a chemotaxis model with local sensing and possibly nonlinear diffusion when the intrinsic diffusion rate ϕ dominates the inverse of the chemotactic motility function γ, in the sense that (ϕγ)'≥ 0. This result encompasses and complies with the analysis and numerical simulations performed in Choi & Kim (2023). The proof involves two steps: first, a Liapunov functional is constructed when ϕγ is non-decreasing. The convergence proof relies on a detailed study of the dissipation of the Liapunov functional and requires additional technical assumptions on ϕ and γ.

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