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2014 Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth
Haiyan Gao, Shengmao Fu
Abstr. Appl. Anal. 2014(SI66): 1-11 (2014). DOI: 10.1155/2014/248657


This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d -dimensional box T d = ( 0 , π ) d ( d = 1,2 , 3 ) . It is proved that given any general perturbation of magnitude δ , its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln ( 1 / δ ) . Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns.


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Haiyan Gao. Shengmao Fu. "Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth." Abstr. Appl. Anal. 2014 (SI66) 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07021993
MathSciNet: MR3230512
Digital Object Identifier: 10.1155/2014/248657

Rights: Copyright © 2014 Hindawi


Vol.2014 • No. SI66 • 2014
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