Nonlocal interactions by repulsive-attractive potentials: Radial ins/stability
Nonlocal interactions by repulsive-attractive potentials: Radial ins/stability
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DOI：
10.1016/j.physd.2012.10.002
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发表时间：
2013-10-01
影响因子：
4
通讯作者：
Raoul, G.
中科院分区：
文献类型：
--
作者：
Balague, D.;Carrillo, J. A.;Raoul, G.
我们研究了具有排斥-吸引径向势的非局部相互作用方程。这样的方程描述了连续密度粒子的演化，它们在其中相互排斥。在短时间内相互吸引（回应）。长)的范围内。我们证明了在势的某些条件下，径向对称解在向球壳定态的一定输运距离内以指数速度收敛。否则，我们证明了径向对称解不可能向球壳定态弱收敛。我们还研究了在什么条件下非径向对称解可能收敛于一般超曲面上的奇异定态。最后给出了具体情况下的排斥-吸引幂律势的详细分析和数值结果。(c) 2012 Elsevier B.V.版权所有
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.