Stationary States of an Aggregation Equation with Degenerate Diffusion and Bounded Attractive Potential
Stationary States of an Aggregation Equation with Degenerate Diffusion and Bounded Attractive Potential
复制标题
具有简并扩散和有界吸引势的聚集方程的稳态
DOI：
10.1137/16m1072450
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Gunnar Kaib
中科院分区：
文献类型：
--
作者：
Gunnar Kaib
研究了一类具有退化幂律扩散和有界吸引势的非局部聚集方程在任意维数下的定态解。紧固定的解决方案的特点和紧凑性的考虑是用来推导出存在相应的能量依赖于退化扩散的前因子的退化扩散的所有指数大于1的全局极小。我们证明了一个全局极小是紧支撑的，在二次扩散的情况下，我们证明了它是唯一的固定解的平移。讨论了仅为局部极小的平稳解的存在性。
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness considerations are used to derive the existence of global minimizers of the corresponding energy depending on the prefactor of the degenerate diffusion for all exponents of the degenerate diffusion greater than one. We show that a global minimizer is compactly supported and, in case of quadratic diffusion, we prove that it is the unique stationary solution up to a translation. The existence of stationary solutions being only local minimizers is discussed.
影响因子：
3.1
作者：
Carrillo, J. A.;Hittmeir, S.;Yao, Y.
通讯作者：
Yao, Y.
影响因子：
2.5
作者：
Balague, D.;Carrillo, J. A.;Raoul, G.
通讯作者：
Raoul, G.