A mathematical characterization for patterns of a Keller-Segel model with a cubic source term
type: Item
instance of: scholarly article
title: A mathematical characterization for patterns of a Keller-Segel model with a cubic source term
zbMATH Open document ID: 1274.92011
DOI: 10.1155/2013/934745
author: Shengmao Fu
author: Ji Liu
published in: Advances in Mathematical Physics
publication date: 2013-06-07T00:00:00Z
review text: Summary: This paper deals with a Neumann boundary value problem for a Keller-Segel model with a cubic source term in a \(d\)-dimensional box (\(d = 1, 2, 3\)), which describes the movement of cells in response to the presence of a chemical signal substance. It is proved that, given any general perturbation of magnitude \(\delta\), 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 \(\ln(1/\delta)\). Each initial perturbation certainly can behave drastically differently from another, which gives rise to the richness of patterns. Our results provide a mathematical description for early pattern formation in the model.
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 35K51
zbMATH DE Number: 6171650
Wikidata QID: Q58918904
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/934745
OpenAlex ID: W1999101506
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description: scientific article; zbMATH DE number 6171650