Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

D. Balagué Guardia, A.B.T. Barbaro, Jose Antonio Carrillo, Robert Volkin

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
36 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)2628–2657
Number of pages30
JournalSIAM Journal on Applied Dynamical Systems
Issue number4
Publication statusPublished - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Aggregation equation
  • Gradient flow
  • Spherical shells


Dive into the research topics of 'Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation'. Together they form a unique fingerprint.

Cite this