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An eigenvalue problem arising from spiky steady states of a minimal chemotaxis model |
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| Authors: | Yajing Zhang Xinfu Chen Jianghao Hao Xin Lai Cong Qin |
| Affiliation: | 1. School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;3. Department of Mathematics, Harbin Institute of Technology, Heilongjiang, 150001, PR China;4. Center for Financial Engineering, Soochow University, Suzhou, 215006, PR China |
| Abstract: | Asymptotic expansion of singular integrals is presented for the study of the existence and uniqueness of spiky steady states of Keller–Segel's minimal chemotaxis model. A tool is developed to find asymptotic expansion of eigenpairs of a nonlocal singular eigenvalue problem arising from the study of stability of the spiky steady state. New insights are given to simplify significantly the proofs of the main results in [1]. |
| Keywords: | Eigenvalue Singular perturbation Asymptotic expansion Chemotaxis |
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