Volume 54, June 2016Gradient flows: from theory to application
|Page(s)||18 - 44|
|Published online||02 August 2016|
Scalar conservation laws seen as gradient flows: known results and new perspectives
Department of Information Engineering, Computer Science, and Mathematics - Via Vetoio 1, I-67100 L'Aquila, Italy
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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.
© EDP Sciences, SMAI 2016
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