Skeleton for the one-dimensional aggregation equation

Abstract

For the aggregation equation in $\mathbb{R}$, we consider the evolution of an initial density corresponding to the characteristic function of some set ${\Omega }_0$. We study the limit measure at the blow up time 1 for ${\Omega }_0$ open or compact and we inspect the limit set (skeleton) where this measure is supported.

v2: the introduction has been improved and the statement of the theorems is done for a more general situation