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.
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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.
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