Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model
Fernandez, Javier; Escobedo, Miguel; Dolbeault, Jean; Blanchet, Adrien (2010), Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model, Journal of Mathematical Analysis and Applications, 361, 2, p. 533-542. http://dx.doi.org/10.1016/j.jmaa.2009.07.034
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00349216/fr/
Journal nameJournal of Mathematical Analysis and Applications
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Abstract (EN)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.
Subjects / KeywordsIntermediate Asymptotics; Self-similar Solution; Drift-diffusion; Chemotaxis; Keller-Segel Model; Entropy; Free Energy; Rate of Convergence; Heat Kernel
Showing items related by title and author.
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions Blanchet, Adrien; Dolbeault, Jean; Perthame, Benoît (2006) Article accepté pour publication ou publié