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We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier.
Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
Y. Yang, B. Engquist, J. Sun, and B. F. Hamfeldt · 1902
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An elementary proof of the polar factorization of vector-valued functions
W. Gangbo · 1994
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The geometry of optimal transportation
W. Gangbo and R. J. McCann · 1996
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A Computational Fluid Mechanics Solution to the Monge-Kantorovich Mass Transfer Problem
J.-D. Benamou and Y. Brenier · 2000
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Numerical resolution of an “unbalanced” mass transport problem
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Partial L1 Monge–Kantorovich problem: Variational formulation and numerical approximation
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