Advances in Differential Equations
- Adv. Differential Equations
- Volume 6, Number 10 (2001), 1173-1218.
Singular limit of a chemotaxis-growth model
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.
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. https://projecteuclid.org/euclid.ade/1357140392.