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Spiky Steady States of a Chemotaxis System with Singular Sensitivity

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Abstract

This paper is concerned with the steady state problem of a chemotaxis model with singular sensitivity function in a one dimensional spatial domain. Using the chemotactic coefficient \(\chi \) as the bifurcation parameter, we perform local and global bifurcation analysis for the model. It is shown that positive monotone steady states exist as long as \(\chi \) is larger than the first bifurcation value \(\bar{\chi }_1.\) We further obtain asymptotic profiles of these steady states, as \(\chi \) becomes large. In particular, our results show that the cell density function forms a spike, which models the important physical phenomenon of cell aggregation.

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Authors and Affiliations

  1. Center for Partial Differential Equations, East China Normal University, 500 Dongchuan Road, Minhang, Shanghai, 200241, People’s Republic of China

    Huicong Li

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  1. Huicong Li
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Correspondence to Huicong Li.

Additional information

This project is partially supported by China Postdoctoral Science Foundation (No. 2016M590335) and National Natural Science Foundation of China (Nos. 11701180 and 11671144).

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Li, H. Spiky Steady States of a Chemotaxis System with Singular Sensitivity. J Dyn Diff Equat 30, 1775–1795 (2018). https://doi.org/10.1007/s10884-017-9621-3

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  • DOI: https://doi.org/10.1007/s10884-017-9621-3

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