Journal article
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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
-
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(Preview, Accepted manuscript, pdf, 709.9KB, Terms of use)
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- Publisher copy:
- 10.1137/20M1314549
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Applied Dynamical Systems More from this journal
- Volume:
- 19
- Issue:
- 4
- Pages:
- 2628–2657
- Publication date:
- 2020-11-19
- Acceptance date:
- 2020-09-03
- DOI:
- ISSN:
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1536-0040
- Language:
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English
- Keywords:
- Pubs id:
-
1131118
- Local pid:
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pubs:1131118
- Deposit date:
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2020-09-08
- ARK identifier:
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2020
- Rights statement:
- © 2020, Society for Industrial and Applied Mathematics
- Notes:
- This is the accepted manuscript version of the article. The final version is available from the Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/20M1314549
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