A one-dimensional Keller-Segel equation with a drift issued from the boundary

Vincent Calvez 1, 2 Nicolas Meunier 3
2 NUMED - Numerical Medicine
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).
Type de document :
Pré-publication, Document de travail
MAP5 2009-23. short version, 8 pages. 2009
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Contributeur : Vincent Calvez <>
Soumis le : vendredi 16 octobre 2009 - 16:31:20
Dernière modification le : mercredi 12 octobre 2016 - 01:17:06
Document(s) archivé(s) le : mardi 15 juin 2010 - 22:46:36

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  • HAL Id : hal-00424649, version 1
  • ARXIV : 0910.3324

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Vincent Calvez, Nicolas Meunier. A one-dimensional Keller-Segel equation with a drift issued from the boundary. MAP5 2009-23. short version, 8 pages. 2009. <hal-00424649>

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