Existence and instability of traveling pulses of Keller-Segel system with nonlinear chemical gradients and small diffusions

Chueh Hsin Chang, Yu Shuo Chen, John M. Hong, Bo Chih Huang

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this paper, we consider a generalized model of 2 × 2 KellerSegel system with a nonlinear chemical gradient and small cell diffusion. The existence of the traveling pulses for such equations is established by the methods of geometric singular perturbation (GSP) and trapping regions from dynamical systems theory. By the technique of GSP, we show that the necessary condition for the existence of traveling pulses is that their limiting profiles with vanishing diffusion can only consist of the slow flows on the critical manifold of the corresponding algebraic-differential system. We also consider the linear instability of these pulses by the spectral analysis of the linearized operators.

原文???core.languages.en_GB???
頁(從 - 到)143-167
頁數25
期刊Nonlinearity
32
發行號1
DOIs
出版狀態已出版 - 1月 2019

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