Article ; Online: Asymptotic stability of spiky steady states for a singular chemotaxis model with signal-suppressed motility.
Mathematical biosciences and engineering : MBE
2023 Volume 19, Issue 12, Page(s) 13988–14028
Abstract: We study the nonlinear stability of spiky solutions to a chemotaxis model of consumption type with singular signal-suppressed motility in the half space. We show that, when the no-flux boundary condition for the bacteria density and the nonhomogeneous ... ...
Abstract | We study the nonlinear stability of spiky solutions to a chemotaxis model of consumption type with singular signal-suppressed motility in the half space. We show that, when the no-flux boundary condition for the bacteria density and the nonhomogeneous Dirichlet boundary condition for the nutrient are prescribed, this chemotaxis model admits a unique smooth spiky steady state, and it is nonlinearly stable under appropriate perturbations. The challenge of the problem is that there are two types of singularities involved in the model: one is the logarithmic singularity of the sensitive function; and the other is the inverse square singularity of the motility. We employ a Cole-Hopf transformation to relegate the former singularity to a nonlocality that can be resolved by the method of anti-derivative. To deal with the latter singularity, we construct an approximate system that retains a key structure of the original singular system in the local theory, and develop a new strategy, which combines a weighted elliptic estimate and the weighted energy estimate, to establish a priori estimate in the global theory. |
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MeSH term(s) | Humans ; Chemotaxis ; Models, Biological ; Hospitalization ; Nutrients |
Language | English |
Publishing date | 2023-01-19 |
Publishing country | United States |
Document type | Journal Article |
ZDB-ID | 2265126-3 |
ISSN | 1551-0018 ; 1551-0018 |
ISSN (online) | 1551-0018 |
ISSN | 1551-0018 |
DOI | 10.3934/mbe.2022652 |
Database | MEDical Literature Analysis and Retrieval System OnLINE |
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