%0 Journal Article
%A Herrero, Miguel A.
%A Medina Reus, Elena
%A Velázquez, J.J. L.
%T Finite-time aggregation into a single point in a reaction-diffusion system
%D 1997
%@ 0951-7715
%U https://hdl.handle.net/20.500.14352/57672
%X 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.
%~