期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 260, 期 -, 页码 5-25出版社
ELSEVIER
DOI: 10.1016/j.physd.2012.10.002
关键词
Repulsive-attractive potentials; Spherical shells; Instability conditions; Radial stability
资金
- Ministerio de Ciencia e Innovacion from Agencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya [MTM2011-27739-C04-02, 2009-SGR-345]
- Royal Society through a Wolfson Research Merit Award
- CBDif-Fr [ANR-08-BLAN-0333-01]
- NSF [DMS-1109805]
- Engineering and Physical Sciences Research Council [EP/K008404/1]
- [KUK-I1- 007-43]
- EPSRC [EP/K008404/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K008404/1] Funding Source: researchfish
We investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse (resp. attract) each other in the short (resp. long) range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. (c) 2012 Elsevier B.V. All rights reserved.
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