In this paper, the one-dimensional Keller-Segel system defined on a bounded interval with the Neumann boundary conditions is considered. The system describes the phenomenon such that the cellular slime molds form an aggregation by the chemotaxis movement. In the case of small chemotaxis, the asymptotic behavior of solutions to the system are analyzed, as the time development, by using the Fourier series. Some of numerical examples are also given.
"Asymptotic Behavior of Solutions to the One-dimensional Keller-Segel System with Small Chemotaxis." Tokyo J. Math. 41 (1) 175 - 191, June 2018. https://doi.org/10.3836/tjm/1502179267