Volume 24, Number 4, October–December 2018
|Page(s)||1415 - 1427|
|Published online||26 October 2018|
On the minimizing movement with the 1-Wasserstein distance
Department of Mathematics and Statistics, University of Victoria,
P.O. Box. 3060 STN CSC,
V8W 3R4, Canada
2 This work was completed after Martial passed away. We wish to dedicate this article to his memory
3 Ceremade, UMR CNRS 7534, Université Paris Dauphine, Pl. de Lattre de Tassigny, 75775, Paris Cedex 16, France, and MOKAPLAN, INRIA-Paris
4 Institut de recherche XLIM-DMI, UMR-CNRS 7252, Faculté des Sciences et Techniques, Université de Limoges 123, Avenue Albert Thomas 87060 Limoges, France
* Corresponding author: firstname.lastname@example.org
Accepted: 22 August 2017
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.
Mathematics Subject Classification: 35K55 / 35D30 / 49N15
Key words: 1-Wasserstein distance / minimizing movement / L1-contraction / growing sandpiles
© EDP Sciences, SMAI 2018
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