Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

Journal article (2020)

Authors

D. Balagué Guardia Numerical Analysis - EEMCS
Alethea Barbaro Mathematical Physics - EEMCS
Jose Antonio Carrillo University of Oxford
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2020 D. Balagué Guardia, Alethea Barbaro, Jose Antonio Carrillo, Robert Volkin
DOI: https://doi.org/10.1137/20M1314549
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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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.

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