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A Computational Fluid Me hani s solution to the

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17 pages
A Computational Fluid Me hani s solution to the Monge-Kantorovi h mass transfer problem. Jean-David Benamou Yann Brenier y July 9, 2001 Abstra t The L 2 Monge-Kantorovi h mass transfer problem [31? is reset in a Fluid Me hani s framework and numeri ally solved by an augmented La- grangian method. 1 Introdu tion The rst mass transfer problem was onsidered by Monge in 1781 in his \memoire sur la theorie des deblais et des remblais, a Civil Engineering problem where par els of materials have to be displa ed from one site to another one with minimal transportation ost. A modern treatment of this problem has been initiated by Kantorovi h in 1942 ( f. [23? for the english version), leading to the so- alled Monge-Kantorovi h problem whi h has re eived a onsiderable interest in the re ent years, with a wide range of potential appli ations and extensions. A re ent omprehensive review an be found in the new books by Ra hev and Rus hendorf [31?, the le ture notes by Evans [19? and the review paper by M Cann and Gangbo [21?. The framework of the Monge-Kantorovi h problem is as follows. Two density fun tions 0 (x) 0 and T (x) 0 of x 2 R d , that we assume to be bounded with total mass one Z

  • fun tions

  • ee tive

  • tive proof

  • problem

  • monge-ampere equation

  • lagrangian method

  • problem has

  • standard boundary

  • alled alg2

  • numeri al


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0
A

Computational
78153
Fluid
review

one

erique,
solution

to
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Monge-Kan
(
toro
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follo
Jean-Da
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vid
to
Benamou
)


Y
:Jean-
ann
aris
Brenier
05,
y
t
July
in
9,

2001


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;
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ersitaire
emoire
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see,
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of
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onds
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asserstein)



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ysics


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w
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dx;
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h
where
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denotes
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