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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.