Geodesic
Scalar conservation laws seen as gradient flows: known results and new perspectives
Marco Di Francesco1
1 Department of Information Engineering, Computer Science, and Mathematics - Via Vetoio 1, I-67100 L'Aquila, Italy
ESAIM. Proceedings, Tome 54 (2016), pp. 18-44.

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We review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory. In particular, we consider the problem of writing a scalar conservation law within the Wasserstein gradient flow theory. As a related problem, we also review results on contraction properties of scalar conservation laws in the p-Wasserstein distances. Moreover, we provide a particle-based approach to view a scalar conservation law as a gradient flow in a nonlinear-mobility sense. Finally, we propose a semi-implicit particle method based on the standard 2-Wasserstein distance.
DOI : 10.1051/proc/201654018

Marco Di Francesco 1

1 Department of Information Engineering, Computer Science, and Mathematics - Via Vetoio 1, I-67100 L'Aquila, Italy 
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Marco Di Francesco. Scalar conservation laws seen as gradient flows: known results and new perspectives. ESAIM. Proceedings, Tome 54 (2016), pp. 18-44. doi : 10.1051/proc/201654018. http://geodesic.mathdoc.fr/articles/10.1051/proc/201654018/

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