On Cross-Diffusion Systems for Two Populations Subject to a Common Congestion Effect
On Cross-Diffusion Systems for Two Populations Subject to a Common Congestion Effect
复制标题
关于受共同拥塞效应影响的两个群体的交叉扩散系统
DOI：
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发表时间：
2017
影响因子：
1.8
通讯作者：
M. Laborde
中科院分区：
文献类型：
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作者：
M. Laborde
本文研究一类通过非线性拥挤耦合的Fokker-Planck方程组解的存在性。考虑了两种不同类型的拥塞：多孔介质拥塞或软拥塞和由约束$$给出的硬拥塞。
ho_（1+）
ho_2左斜1$$ ρ 1 + ρ 2 ρ 1。我们表明，这些系统可以看作是梯度流在Wasserstein产品空间，然后我们得到一个建设性的方法来证明解的存在性。因此，它是自然的，将其应用于数值目的，并包括一些数值模拟。
In this paper, we investigate the existence of solution for systems of Fokker–Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or soft congestion and the hard congestion given by the constraint $$
ho _1+
ho _2 leqslant 1$$ ρ 1 + ρ 2 ⩽ 1 . We show that these systems can be seen as gradient flows in a Wasserstein product space and then we obtain a constructive method to prove the existence of solutions. Therefore it is natural to apply it for numerical purposes and some numerical simulations are included.