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Volume 37, Issue 1
Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit

Zefu Feng, Jiao Xu, Ling Xue & Kun Zhao

DOI: 10.4208/aam.OA-2020-0004

Ann. Appl. Math., 37 (2021), pp. 61-110.

Published online: 2021-02

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  • 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.

  • Keywords

Balance laws, chemotaxis, initial-boundary value problem, dynamic boundary condition, strong solution, long-time behavior, diffusivity limit.

  • AMS Subject Headings

35B40, 35K51, 35Q92

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zefufeng@mails.ccnu.edu.cn (Zefu Feng)

xuj7@sustech.edu.cn (Jiao Xu)

lxue@hrbeu.edu.cn (Ling Xue)

kzhao@tulane.edu (Kun Zhao)

  • BibTex
  • RIS
  • TXT
@Article{AAM-37-61, author = {Feng , ZefuXu , JiaoXue , Ling and Zhao , Kun}, title = {Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {37}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2020-0004}, url = {http://global-sci.org/intro/article_detail/aam/18631.html} }
TY - JOUR T1 - Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit AU - Feng , Zefu AU - Xu , Jiao AU - Xue , Ling AU - Zhao , Kun JO - Annals of Applied Mathematics VL - 1 SP - 61 EP - 110 PY - 2021 DA - 2021/02 SN - 37 DO - http://doi.org/10.4208/aam.OA-2020-0004 UR - https://global-sci.org/intro/article_detail/aam/18631.html KW - Balance laws, chemotaxis, initial-boundary value problem, dynamic boundary condition, strong solution, long-time behavior, diffusivity limit. AB -

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.

Feng , ZefuXu , JiaoXue , Ling and Zhao , Kun. (2021). Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis: Global Dynamics and Diffusivity Limit. Annals of Applied Mathematics. 37 (1). 61-110. doi:10.4208/aam.OA-2020-0004
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