Spectral analysis for stability of bubble steady states of a Keller-Segel's minimal chemotaxis model

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• 作者：Yajing Zhang^a ; ^{zhangyj@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xinfu Chen^b ; ^{xinfu@pitt.edu" class="auth_mail" title="E-mail the corresponding author} ; Jianghao Hao^a ; ^{hjhao@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xin Lai^c ; ^{laixin2002@163.com" class="auth_mail" title="E-mail the corresponding author} ; Cong Qin^d ; ^{wacilee.qin@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Spectral analysis ; Elliptic system ; Stability ; Chemotaxis ; Relaxation parameter
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：1105-1132
• 全文大小：545 K

文摘

A number of techniques, some of which are novel, are introduced to develop a systematic method to study a set of eigenvalue problems arising from the stability analysis of bubble steady states of a Keller–Segel's minimal chemotaxis model. Estimates of the eigenvalue with largest real part of an elliptic system without variational structure and the second eigenvalue of a corresponding subproblem possessing variational structure are obtained. These estimates provide critical information about the stability of the bubble steady state with respect to the time relaxation parameter; in particular, it is shown that the stability decreases to zero as the relaxation parameter goes to infinity.