Year: 2025
Author: Jingyu Li, Zhi-An Wang
CSIAM Transactions on Life Sciences, Vol. 1 (2025), Iss. 1 : pp. 153–178
Abstract
In this paper, we establish the existence and nonlinear stability of a hyperbolic system of conservation laws derived from a repulsive singular chemotaxis model. By the phase plane analysis alongside Poincaré-Bendixson theorem, we first prove that this hyperbolic system admits three different types of traveling wave profiles, which are explicitly illustrated with numerical simulations. Then using a unified weighted energy estimates and technique of taking anti-derivatives, we prove that all types of traveling wave profiles, including non-monotone pulsating wave profiles, are nonlinearly and asymptotically stable if the initial data are small perturbations with zero mass from the spatially shifted traveling wave profiles.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-ls.SO-2024-0005a
CSIAM Transactions on Life Sciences, Vol. 1 (2025), Iss. 1 : pp. 153–178
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Chemotaxis conservation laws traveling waves nonlinear stability weighted energy estimates.