Multiple Stable Traveling Wave Profiles of a System of Conservation Laws Arising from Chemotaxis
Year: 2025
Type: article
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.
Authors: Jingyu Li, Zhi-An Wang
Institutions: Northeast Normal University, Hong Kong Polytechnic University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4408812239