Advances in Differential Equations

Singular limit of a chemotaxis-growth model

A. Bonami, D. Hilhorst, E. Logak, and M. Mimura

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We consider a reaction-diffusion-advection system which is a model for chemotaxis with growth. An appropriate singular limit of this system yields a free-boundary problem where the interface motion depends on the mean curvature and on some nonlocal term. We prove local-in-time existence, uniqueness and regularity for this free-boundary problem and investigate some qualitative properties (lack of monotonicity, loss of convexity). We then establish the convergence of the solution of the reaction-diffusion-advection system to the solution of the free-boundary problem.

Article information

Adv. Differential Equations, Volume 6, Number 10 (2001), 1173-1218.

First available in Project Euclid: 2 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35B25: Singular perturbations 35B50: Maximum principles 35R35: Free boundary problems 92C15: Developmental biology, pattern formation 92C17: Cell movement (chemotaxis, etc.)


Bonami, A.; Hilhorst, D.; Logak, E.; Mimura, M. Singular limit of a chemotaxis-growth model. Adv. Differential Equations 6 (2001), no. 10, 1173--1218.

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