Multiple peak aggregations for the Keller-Segel system

TL;DR

This paper develops matched asymptotic expansions for the Keller-Segel system in 2D with multiple aggregation peaks, extending previous work limited to a single peak case, and providing new insights into multi-peak mass aggregation behavior.

Contribution

It introduces the first asymptotic analysis for multi-peak solutions of the Keller-Segel system in two dimensions, generalizing prior single-peak results.

Findings

Derived asymptotic expansions for N-peak solutions

Extended understanding of mass aggregation in the Keller-Segel model

Provided mathematical framework for multi-peak behavior

Abstract

In this paper we derive matched asymptotic expansions for a solution of the Keller-Segel system in two space dimensions for which the amount of mass aggregation is $8\pi N$, where $N=1,2,3,...$ Previously available asymptotics had been computed only for the case in which N=1.