Transition Layers to Chemotaxis-Consumption Models with Volume-Filling Effect
Year: 2024
Author: Xiaowen Li, Jingyu Li
Journal of Mathematical Study, Vol. 57 (2024), Iss. 3 : pp. 331–357
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n3.24.06
Journal of Mathematical Study, Vol. 57 (2024), Iss. 3 : pp. 331–357
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Chemotaxis volume-filling transition layer stability physical boundary conditions.
Author Details
Xiaowen Li Email
Jingyu Li Email