Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk
| dc.creator | Kavallaris, Nikos | |
| dc.creator | Souplet, Philippe | |
| dc.date | 2008-04-29 | |
| dc.date | 2008-09-05 | |
| dc.date.accessioned | 2026-07-07T10:00:33Z | |
| dc.date.available | 2026-07-07T10:00:33Z | |
| dc.description | We consider a special case of the Patlak-Keller-Segel system in a disc, which arises in the modelling of chemotaxis phenomena. For a critical value of the total mass, the solutions are known to be global in time but with density becoming unbounded, leading to a phenomenon of mass-concentration in infinite time. We establish the precise grow-up rate and obtain refined asymptotic estimates of the solutions. Unlike in most of the similar, recently studied, grow-up problems, the rate is neither polynomial nor exponential. In fact, the maximum of the density behaves like $e^{\sqrt{2t}}$ for large time. In particular, our study provides a rigorous proof of a behaviour suggested by Sire and Chavanis [Phys. Rev. E, 2002] on the basis of formal arguments. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0804.4549 | |
| dc.identifier | http://arxiv.org/abs/0804.4549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168349 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K60, 35B40, 92C17 (Primary); 35Q72 (Secondary) | |
| dc.title | Grow-up rate and refined asymptotics for a two-dimensional Patlak-Keller-Segel model in a disk | |
| dc.type | text |