Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation
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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Published In
SIAM Journal on Applied Dynamical Systems
Pages: 2628 - 2657
DOI: 10.1137/20M1314549
ISSN (online): 1536-0040
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© 2020, Society for Industrial and Applied Mathematics.
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Submitted: 22 January 2020
Accepted: 2 September 2020
Published online: 19 November 2020
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Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/P031587/1
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European Research Council https://doi.org/10.13039/501100000781 : 883363
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National Science Foundation https://doi.org/10.13039/100000001 : DMS-1319462
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