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hal-00585231, version 1

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

Matthieu Alfaro () 1, Elisabeth Logak () 2

Abstract: 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.

  • 1:  Institut de Mathématiques et de Modélisation de Montpellier (I3M)
  • CNRS : UMR5149 – Université Montpellier II - Sciences et techniques
  • 2:  Laboratoire d'Analyse, Géométrie et Modélisation (AGM)
  • CNRS : UMR8088 – Université de Cergy Pontoise
 
  • hal-00585231, version 1
  • http://hal.archives-ouvertes.fr/hal-00585231
  • oai:hal.archives-ouvertes.fr:hal-00585231
  • From: Matthieu Alfaro <>
  • Submitted on: Tuesday, 12 April 2011 11:15:53
  • Updated on: Tuesday, 12 April 2011 11:27:37