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Multiple peak aggregations for the Keller–Segel system

Multiple peak aggregations for the Keller–Segel system

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 8πN, where N = 1, 2, 3, ... Previously available asymptotics had been computed only for the case in which N = 1.