Nonlinear stability of spiky patterns to a chemotaxis-consumption model with signal-dependent motilities

Song, Xu1; Li, Jingyu2; Zhang, Tianbo3

2024-11-05

10.1016/j.jde.2024.06.033

JOURNAL OF DIFFERENTIAL EQUATIONS   影响因子和分区

0022-0396

1090-2732

This paper is concerned with the dynamical stability of spiky steady states to a chemotaxis-consumption model with signal-dependent motilities on the half space, where no-flux boundary condition for the bacteria and inhomogeneous Dirichlet boundary condition for the nutrient are prescribed. The motilities of bacteria depend on the concentration of nutrient in the form of power law, which means that they are degenerate if the power-law exponent is positive and are singular if the exponent is negative at the zero state of nutrient. We show that in both cases the spiky patterns admitted by the model are nonlinearly stable under appropriate perturbations. We introduce a unified approach to dealing with both degeneracy and singularity in the diffusivity for this model. The approach is based on a combination of weighted energy estimates and weighted elliptic estimates, where various weights are artfully constructed to capture the complex behaviors of solutions near the zero state. Numerical simulations are also carried out to confirm our theoretical results. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Chemotaxis Signal -dependent motility Degeneracy Spike Nonlinear stability

SCI

英语

第一

Shenzhen Science and Technology Innovation Commission[20220814171825001] ; National Natural Science Foundation of China[12371216] ; Natural Science Foundation of Jilin Province[20210101144JC]

Mathematics

Mathematics

WOS:001267988000001

ACADEMIC PRESS INC ELSEVIER SCIENCE

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China
3.Univ Washington, Dept Appl Math, Seattle, WA 98105 USA

Song, Xu,Li, Jingyu,Zhang, Tianbo. Nonlinear stability of spiky patterns to a chemotaxis-consumption model with signal-dependent motilities[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2024,408.

Song, Xu,Li, Jingyu,&Zhang, Tianbo.(2024).Nonlinear stability of spiky patterns to a chemotaxis-consumption model with signal-dependent motilities.JOURNAL OF DIFFERENTIAL EQUATIONS,408.

Song, Xu,et al."Nonlinear stability of spiky patterns to a chemotaxis-consumption model with signal-dependent motilities".JOURNAL OF DIFFERENTIAL EQUATIONS 408(2024).