@Article{CSIAM-LS-1-153,
author = {Li , Jingyu and Wang , Zhi-An},
title = {Multiple Stable Traveling Wave Profiles of a System of Conservation Laws Arising from Chemotaxis},
journal = {CSIAM Transactions  on Life Sciences},
year = {2025},
volume = {1},
number = {1},
pages = {153--178},
abstract = {<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>},
issn = {3006-2721},
doi = {https://doi.org/10.4208/csiam-ls.SO-2024-0005a},
url = {http://global-sci.org/intro/article_detail/csiam-ls/23914.html}
}