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 - <p style="text-align: justify;">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.</p>