Confinement for repulsive-attractive kernels

Daniel Balagué; José A. Carrillo; Yao Yao

doi:10.3934/dcdsb.2014.19.1227

Article Contents

2014, Volume 19, Issue 5: 1227-1248. Doi: 10.3934/dcdsb.2014.19.1227

This issue Previous Article Preface to special issue on mathematics of social systems Next Article Phase transition and diffusion among socially interacting self-propelled agents

Confinement for repulsive-attractive kernels

1.
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205
2.
Department of Mathematics, Imperial College, London, London SW7 2AZ
3.
Department of Mathematics, University of Wisconsin, Madison, WI 53706

Received: July 31, 2012

Revised: October 31, 2012

Published: June 2014

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Abstract

We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the potential. The arguments apply to the functional setting of probability measures with mildly singular repulsive-attractive potentials and to the functional setting of smooth solutions with a potential being the sum of the Newtonian repulsion at the origin and a smooth suitably growing at infinity attractive potential.

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Mathematics Subject Classification: Primary: 35Q92; Secondary: 35B40, 37N25.

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