Skeleton for the one-dimensional aggregation equation

Abstract

Abstract For the aggregation equation in $$\mathbb {R}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>R</mml:mi> </mml:math> , we consider the evolution of an initial density corresponding to the characteristic function of some set $$\Omega _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . We study the limit measure at the blow up time 1 for $$\Omega _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> open or compact and we inspect the limit set (skeleton) where this measure is supported.

Locations

• Analysis and Mathematical Physics - View - PDF