BOUNDEDNESS AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS

作     者：Jie JIANG 江杰

作者机构：Innovation Academy for Precision Measurement Science and TechnologyCASWuhan 430071China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第3期

页      面：825-846页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Hubei Provincial Natural Science Foundation(2020CFB602) 

主　　题：Classical solution boundedness exponential stabilization degeneracy Keller-Segel models 

摘      要：In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility *** main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes *** the current work,we are interested in the boundedness and exponential stability of the classical solution in higher *** the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases *** we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted ***,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady *** boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.