TY - JOUR
T1 - Transition Layers to Chemotaxis-Consumption Models with Volume-Filling Effect
AU - Li , Xiaowen
AU - Li , Jingyu
JO - Journal of Mathematical Study
VL - 3
SP - 331
EP - 357
PY - 2024
DA - 2024/10
SN - 57
DO - http://doi.org/10.4208/jms.v57n3.24.06
UR - https://global-sci.org/intro/article_detail/jms/23492.html
KW - Chemotaxis, volume-filling, transition layer, stability, physical boundary conditions.
AB - <p style="text-align: justify;">We are interested in the dynamical behaviors of solutions to a parabolic-parabolic chemotaxis-consumption model with a volume-filling effect on a bounded
interval, where the physical no-flux boundary condition for the bacteria and mixed
Dirichlet-Neumann boundary condition for the oxygen are prescribed. By taking a
continuity argument, we first show that the model admits a unique nonconstant steady
state. Then we use Helly’s compactness theorem to show that the asymptotic profile of
steady state is a transition layer as the chemotactic coefficient goes to infinity. Finally,
based on the energy method along with a cancellation structure of the model, we show
that the steady state is nonlinearly stable under appropriate perturbations. Moreover,
we do not need any assumption on the parameters in showing the stability of steady
state.</p>