Convergence to a propagating front in a degenerate Fisher-KPP equation with advection

Matthieu Alfaro (1) , Elisabeth Logak (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis-growth model. We study its behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We analyze, for small times, the emergence of transition layers induced by a balance between reaction and drift effects. Then we investigate the propagation of the layers. Convergence to a free-boundary limit problem is proved and a sharp estimate of the thickness of the layers is provided.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Alfaro, Elisabeth Logak. Convergence to a propagating front in a degenerate Fisher-KPP equation with advection. Journal of Mathematical Analysis and Applications, 2012, 387 (1), pp.251-266. ⟨10.1016/j.jmaa.2011.08.068⟩. ⟨hal-00585231v2⟩