论文标题
具有非线性迁移的最佳运输：确定性粒子近似结果
Optimal transport with nonlinear mobilities: a deterministic particle approximation result
论文作者
论文摘要
我们通过在n有序粒子的锥体上通过适当的离散指标在实际线上在实际线上具有非线性迁移率的广义瓦斯恒星距离的离散化，这种设置自然出现在偏微分方程的确定性粒子近似框架中。特别是，我们为相关的离散指标提供了$γ$ convergence的结果，作为$ n \ to \ infty $向连续的$提供，并通过所谓的普遍最小化的运动来讨论（梯度流类型）的近似（梯度流量类型）的近似，证明了在任何定义的iDiveTe diviveet time $ $ $ $ v> 0 $ 0 $ v> 0 $ v。这是旨在在广义梯度 - 流量结构，保护定律和具有非线性迁移率的瓦斯坦斯坦距离之间相互作用的新灯的系列作品。
We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a $Γ$-convergence result for the associated discrete metrics as $N \to \infty$ to the continuous one and discuss applications to the approximation of one-dimensional conservation laws (of gradient flow type) via the so-called generalized minimizing movements, proving a convergence result of the schemes at any given discrete time step $τ>0$. This the first work of a series aimed at shedding new lights on the interplay between generalized gradient-flow structures, conservation laws, and Wasserstein distances with nonlinear mobilities.
