Solutions to Monge-Kantorovich equations as stationary points of a dynamical system

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.

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