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

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