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| HAL : hal-00349216, version 1 |
| arXiv : 0812.4876 |
| DOI : 10.1016/j.jmaa.2009.07.034 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Analysis and applications 361, 2 (2008) 533-542 |
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| Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model |
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| Adrien Blanchet 1Jean Dolbeault 2 |
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| (25/12/2008) |
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| The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less $8\pi\,$, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar~variables. |
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| 1 : | Groupe de recherche en économie mathématique et quantitative (GREMAQ) |
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CNRS : UMR5604 – Université des Sciences Sociales - Toulouse I – École des Hautes Études en Sciences Sociales [EHESS] – Institut national de la recherche agronomique (INRA) : UMR |
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| 2 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 3 : | Departamento de Matematicas |
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Universidad del País Vasco |
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| 4 : | Departamento Automatica y Computacion |
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Universidad Pública de Navarra |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00349216, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00349216 | |
| oai:hal.archives-ouvertes.fr:hal-00349216 | |
| Contributeur : Adrien Blanchet | |
| Soumis le : Mercredi 24 Décembre 2008, 16:47:29 | |
| Dernière modification le : Mercredi 27 Octobre 2010, 23:39:58 | |
