On the minimizing movement with the 1-Wasserstein distance
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1415-1427.

We consider a class of doubly nonlinear constrained evolution equations which may be viewed as a nonlinear extension of the growing sandpile model of [L. Prigozhin, Eur. J. Appl. Math.  7 (1996) 225–235.]. We prove existence of weak solutions for quite irregular sources by a semi-implicit scheme in the spirit of the seminal works of [R. Jordan et al., SIAM J. Math. Anal.  29 (1998) 1–17, D. Kinderlehrer and N.J. Walkington, Math. Model. Numer. Anal.  33 (1999) 837–852.] but with the 1-Wasserstein distance instead of the quadratic one. We also prove an L1-contraction result when the source is L1 and deduce uniqueness and stability in this case.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017055
Classification : 35K55, 35D30, 49N15
Mots-clés : 1-Wasserstein distance, minimizing movement, L1-contraction, growing sandpiles
Agueh, Martial 1 ; Carlier, Guillaume 1 ; Igbida, Noureddine 1

1 
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Agueh, Martial; Carlier, Guillaume; Igbida, Noureddine. On the minimizing movement with the 1-Wasserstein distance. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1415-1427. doi : 10.1051/cocv/2017055. http://archive.numdam.org/articles/10.1051/cocv/2017055/

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