Solutions to Monge-Kantorovich equations as stationary points of a dynamical system
Solutions to Monge-Kantorovich equations as stationary points of a dynamical system
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作为动力系统驻点的 Monge-Kantorovich 方程的解
DOI：
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发表时间：
2005
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通讯作者：
L. Prigozhin
中科院分区：
文献类型：
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作者：
L. Prigozhin
Monge-Kantorovich方程的解是沙面演化临界坡度模型的稳定点，该方程表达了费用等于距离的大规模运输问题的最优性条件。利用沙粒模型的对偶变分公式，分别计算了最优输运密度和Kantorovich势作为演变沙粒通量和沙粒表面的t → ∞极限。
Solutions to Monge-Kantorovich equations, expressing optimality condition in mass transportation problem with cost equal to distance, are stationary points of a critical-slope model for sand surface evolution. Using a dual variational formulation of sand model, we compute both the optimal transport density and Kantorovich potential as t → ∞ limit of evolving sand flux and sand surface, respectively.