Advances in Differential Equations

The singular limit of a chemotaxis-growth system with general initial data

Matthieu Alfaro

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Abstract

We study the singular limit of a system of partial differential equations which is a model for an aggregation of amoebae subjected to three effects: diffusion, growth and chemotaxis. The limit problem involves motion by mean curvature together with a nonlocal drift term. We consider rather general initial data. We prove a generation of interface property and study the motion of interfaces. We also obtain an optimal estimate of the thickness and the location of the transition layer that develops.

Article information

Source
Adv. Differential Equations Volume 11, Number 11 (2006), 1227-1260.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867596

Mathematical Reviews number (MathSciNet)
MR2277063

Zentralblatt MATH identifier
1153.35010

Subjects
Primary: 35K50
Secondary: 35B50: Maximum principles 35K57: Reaction-diffusion equations 35R35: Free boundary problems 92C17: Cell movement (chemotaxis, etc.)

Citation

Alfaro, Matthieu. The singular limit of a chemotaxis-growth system with general initial data. Adv. Differential Equations 11 (2006), no. 11, 1227--1260. https://projecteuclid.org/euclid.ade/1355867596.


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