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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2012

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

Résumé

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.
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Dates et versions

hal-00585231 , version 1 (12-04-2011)
hal-00585231 , version 2 (19-04-2011)

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Citer

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⟩
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