Impacto
Downloads
Downloads per month over past year
Herrero, Miguel A. and Medina Reus, Elena and Velázquez, J.J. L. (1997) Finite-time aggregation into a single point in a reaction-diffusion system. Nonlinearity, 10 (6). pp. 1739-1754. ISSN 0951-7715
![[thumbnail of Herrero30.pdf]](/style/images/fileicons/application_pdf.png) |
PDF
Restringido a Repository staff only 205kB |
Official URL: http://iopscience.iop.org/0951-7715/10/6/016
Abstract
We consider the following system: [GRAPHICS] which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial solutions that blow-up in a finite time. The asymptotic behaviour of such solutions is analysed in detail. In particular, we obtain that the profile of any such solution consists of an imploding, smoothed-out shock wave that collapses into a Dine mass when the singularity is formed. The differences between this type of behaviour and that known to occur for blowing-up solutions of (S) in the case N = 2 are also discussed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Chemotaxis; equations; singularities; clusters |
| Subjects: | Sciences > Mathematics > Differential equations |
| ID Code: | 16970 |
| Deposited On: | 05 Nov 2012 11:29 |
| Last Modified: | 12 Dec 2018 15:08 |
Origin of downloads
Repository Staff Only: item control page
