TY - JOUR
T1 - Multiple Stable Traveling Wave Profiles of a System of Conservation Laws Arising from Chemotaxis
AU - Li , Jingyu
AU - Wang , Zhi-An
JO - CSIAM Transactions  on Life Sciences
VL - 1
SP - 153
EP - 178
PY - 2025
DA - 2025/03
SN - 1
DO - http://doi.org/10.4208/csiam-ls.SO-2024-0005a
UR - https://global-sci.org/intro/article_detail/csiam-ls/23914.html
KW - Chemotaxis, conservation laws, traveling waves, nonlinear stability, weighted energy estimates.
AB - <p style="text-align: justify;">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.</p>