| 概要 | In this talk I will talk about aggregations of Dirac mass in
theKeller-Segel system.
It is common that blow-up takes place under the assumption that the mass
is initially greater than  and the distribution of initial mass is
localized around a point of the domain under consideration. Every blow-up
produces a Dirac mass at the blow-up time. The quantity of the Dirac mass
is, in general, unknown.
We show that it is possible to construct, by matched asymptotic expansion
techniques, a formal solution having two peaks that aggregate at the
blow-up time and thus producing  as the quantity of Dirac mass.
This talk is based on a joint work with Prof. J.J.L. Vel zquez and
Prof. Y. Sugiyama. |