Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime
Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime
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DOI：
10.1512/iumj.2018.67.7524
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发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
J. Carrillo;Y. Sugiyama
中科院分区：
文献类型：
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作者：
J. Carrillo;Y. Sugiyama
我们首先证明，当扩散主导化学引诱剂的吸引力时，与经典 Keller-Segel 模型的非线性扩散版本相关的所有质量存在唯一的自由能全局最小化。该策略通过大半径有界球上提出的最小化问题来近似整个空间中的变分问题。我们表明，一个广泛类别中的所有静止状态都与平移一致，具有独特的紧支撑径向递减和光滑，其支持自由能的全局最小化。我们的结果补充并显示了关于 \cite{Strohmer,LY,Kim-Yao} 的替代证明。
We first show the existence of unique global minimizer of the free energy for all masses associated to a nonlinear diffusion version of the classical Keller-Segel model when the diffusion dominates over the attractive force of the chemoattractant. The strategy uses an approximation of the variational problem in the whole space by the minimization problem posed on bounded balls with large radii. We show that all stationary states in a wide class coincide up to translations with the unique compactly supported radially decreasing and smooth inside its support global minimizer of the free energy. Our results complement and show alternative proofs with respect to \cite{Strohmer,LY,Kim-Yao}.