Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

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

doi:10.1137/20M1314549

Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

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

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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.

Original language	English
Pages (from-to)	2628–2657
Number of pages	30
Journal	SIAM Journal on Applied Dynamical Systems
Volume	19
Issue number	4
DOIs	https://doi.org/10.1137/20M1314549
Publication status	Published - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
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.

Keywords

Aggregation equation
Gradient flow
Spherical shells

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title = "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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note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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. ",

year = "2020",

doi = "10.1137/20M1314549",

language = "English",

volume = "19",

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AU - Balagué Guardia, D.

AU - Barbaro, A.B.T.

AU - Carrillo, Jose Antonio

AU - Volkin, Robert

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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.

PY - 2020

Y1 - 2020

N2 - 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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KW - Gradient flow

KW - Spherical shells

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DO - 10.1137/20M1314549

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JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

IS - 4

ER -

Analysis of Spherical Shell Solutions for the Radially Symmetric Aggregation Equation

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