Singular limits of chemotaxis-growth model
type: Item
instance of: scholarly article
title: Singular limits of chemotaxis-growth model
zbMATH Open document ID: 1001.35052
DOI: 10.1016/S0362-546X(00)00149-8
author: Inwon Kim
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-04-22T00:00:00Z
reviewed by: René Sperb
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 92C45
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 1697583
zbMATH Keywords: chemotaxis-growth model
MaRDI profile type: Publication
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review text: The author studies a system of the form NEWLINE\[NEWLINE\left.\begin{aligned} & u_t= ab\Delta u+\nabla\cdot (u\nabla X(v))+af(u,v)=0\\ & V_t-\varepsilon c(\Delta v-g(u,v))=0\end{aligned}\right\}\quad \text{in }\mathbb{R}^N\times (0,\infty)NEWLINE\]NEWLINE with \(f(u,v)=(u^2-1)(u-\mu)+\sigma v\), \(g(u,v)=\gamma v-u\), \(a=\frac{1}{\varepsilon^2}\), \(c=\frac 1\varepsilon\), \(b=\varepsilon^2\) or \(a=c=\frac 1\varepsilon\), \(b=\varepsilon^2\). The behavior as \(\varepsilon\to 0\) is then studied.
description: scientific article; zbMATH DE number 1697583