Advances in Differential Equations

Singular limit of a chemotaxis-growth model

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

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

Permanent link to this document

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.

Export citation