Physics Commons^™

Stability And Clustering Of Self-Similar Solutions Of Aggregation Equations, Hui Sun, David Uminsky, Andrea L. Bertozzi

Mathematics

In this paper we consider the linear stability of a family of exact collapsing similarity solutions to the aggregation equation ρ _t = ∇ · (ρ∇K * ρ) in Rd , d ⩾ 2, where K(r) = r ^γ/γ with γ > 2. It was previously observed [Y. Huang and A. L. Bertozzi, “Self-similar blowup solutions to an aggregation equation in Rn,” J. SIAM Appl. Math.70, 2582–2603 (Year: 2010)]10.1137/090774495 that radially symmetric solutions are attracted to a self-similar collapsing shell profile in infinite time for γ > 2. In this paper we compute the stability of the …