SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2628-2657, January 2020.
We study distributional solutions to the radially symmetric aggregation equation for power-law potentials. We show that distributions containing spherical shells form part of a basin of attraction in the space of solutions in the sense of “shifting stability." For spherical shell initial data, we prove the exponential convergence of solutions to equilibrium and construct some explicit solutions for specific ranges of attractive power. We further explore results concerning the evolution and equilibria for initial data formed from convex combinations of spherical shells.

中文翻译：

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径向对称聚合方程的球壳解分析

SIAM应用动力系统杂志，第19卷，第4期，第2628-2657页，2020年1月。
我们研究了幂律势的径向对称聚合方程的分布解。我们从“位移稳定性”的意义上说明了包含球形壳的分布在解空间中形成了吸引盆的一部分。对于球形壳初始数据，我们证明了平衡解的指数收敛性，并为特定解构造了一些显式解我们进一步探索有关球形壳凸组合形成的初始数据的演化和平衡的结果。