| 概要 | We deal with the two-dimensional Keller-Segel system
describing chemotaxis
in a bounded domain with smooth boundary under the nonnegative initial data.
As for the Keller-Segel system, the  -norm is the scaling invariant one
for the initial data, and so if the initial data is sufficiently small in
,
then the solution exists globally in time. On the other hand, if its
">L^1">-norm is large,
then the solution blows up in a finite time.
The first purpose of my talk is to construct a time global solution
as a measure valued function beyond the blow-up time
even though the initial data is large in . The second purpose is
to show the existence of two measure valued solutions of the different type
depending on the approximation, while the classical solution is unique
before the blow-up time. |