We introduce a modification of the Monge-Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.
@article{M2AN_2003__37_5_851_0,
author = {Benamou, Jean-David},
title = {Numerical resolution of an ``unbalanced'' mass transport problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {851-868},
doi = {10.1051/m2an:2003058},
zbl = {1037.65063},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_5_851_0}
}
Benamou, Jean-David. Numerical resolution of an “unbalanced” mass transport problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 851-868. doi : 10.1051/m2an:2003058. http://gdmltest.u-ga.fr/item/M2AN_2003__37_5_851_0/
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