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Spiky Steady States of a Chemotaxis System with Singular Sensitivity
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Journal Article
Spiky Steady States of a Chemotaxis System with Singular Sensitivity
2018
Overview
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 χ 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 χ is larger than the first bifurcation value χ¯1. We further obtain asymptotic profiles of these steady states, as χ becomes large. In particular, our results show that the cell density function forms a spike, which models the important physical phenomenon of cell aggregation.
Publisher
Springer Nature B.V
Subject
