Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit
Year: 2021
Author: Zefu Feng, Jiao Xu, Ling Xue, Kun Zhao
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 61–110
Abstract
In this paper, we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation rate. Utilizing energy methods, we show that under time-dependent Dirichlet boundary conditions, long-time dynamics of solutions are driven by their boundary data, and there is no restriction on the magnitude of initial energy. Moreover, the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions, which has not been observed in previous studies on related models.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2020-0004
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 61–110
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 50
Keywords: Balance laws chemotaxis initial-boundary value problem dynamic boundary condition strong solution long-time behavior diffusivity limit.
Author Details
-
Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks
Xue, Ling | Zhang, Min | Zhao, Kun | Zheng, XiaomingCommunications in Nonlinear Science and Numerical Simulation, Vol. 117 (2023), Iss. P.106913
https://doi.org/10.1016/j.cnsns.2022.106913 [Citations: 1] -
Existence and stability of boundary spike layer solutions of an attractive chemotaxis model with singular sensitivity and nonlinear consumption rate of chemical stimuli
Feng, Zefu | Zhao, Kun | Zhou, ShoumingPhysica D: Nonlinear Phenomena, Vol. 471 (2025), Iss. P.134429
https://doi.org/10.1016/j.physd.2024.134429 [Citations: 1] -
Global stability of a system of viscous balance laws arising from chemotaxis with dynamic boundary flux
Zeng, Yanni | Zhao, KunJournal of Differential Equations, Vol. 416 (2025), Iss. P.2221
https://doi.org/10.1016/j.jde.2024.10.037 [Citations: 0] -
Asymptotic nonlinear stability of traveling waves to a chemotaxis model with logarithmic sensitivity and nonlinear production
Zhu, Neng | Wang, Cong | Wang, WanwanPhysica Scripta, Vol. 99 (2024), Iss. 12 P.125292
https://doi.org/10.1088/1402-4896/ad925f [Citations: 0] -
Stability of steady‐state solutions of a class of Keller–Segel models with mixed boundary conditions
Feng, Zefu | Jia, Jing | Zhou, ShoumingMathematical Methods in the Applied Sciences, Vol. 47 (2024), Iss. 12 P.9476
https://doi.org/10.1002/mma.10079 [Citations: 0] -
Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions
Xue, Ling | Zhang, Min | Zhao, Kun | Zheng, XiaomingElectronic Research Archive, Vol. 30 (2022), Iss. 12 P.4530
https://doi.org/10.3934/era.2022230 [Citations: 3] -
Dynamical behaviour of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions
Fuster Aguilera, Padi | Zhao, KunEuropean Journal of Applied Mathematics, Vol. (2024), Iss. P.1
https://doi.org/10.1017/S0956792524000329 [Citations: 1]