期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
卷 19, 期 5, 页码 1227-1248出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2014.19.1227
关键词
Aggregation equation; particle systems; confinement
资金
- Ministerio de Ciencia e Innovacion [MTM2011-27739-C04-02]
- Agencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya [2009-SGR-345]
- Royal Society through a Wolfson Research Merit Award
- Engineering and Physical Sciences Research Council [EP/K008404/1]
- NSF [DMS-0970072, DMS-1104415]
- Engineering and Physical Sciences Research Council [EP/G02684X/1, EP/K008404/1] Funding Source: researchfish
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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