Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
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DOI：
10.1007/s00222-019-00898-x
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发表时间：
2019-12-01
影响因子：
3.1
通讯作者：
Yao, Y.
中科院分区：
文献类型：
--
作者：
Carrillo, J. A.;Hittmeir, S.;Yao, Y.
我们分析在何种条件下两个竞争的影响，排斥建模的非线性扩散和吸引力建模的非局部相互作用之间的平衡，发生。这种平衡导致所有质量的连续压缩支撑径向减少平衡配置。通过连续Steiner对称化技术，所有具有适当规则性的定态都是径向对称的。变分法工具使我们能够显示这些平衡点之间的全局极小值的存在。最后，在二维牛顿相互作用的特殊情况下，它们导致了对于任何给定的质量直到平移的平衡的唯一性，并且导致了相关的非线性聚集扩散方程的解朝着这个直到平移的唯一平衡分布收敛
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the particular case of Newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation-diffusion equations towards this unique equilibrium profile up to translations