Abstract

Motivated by the Derrida-Lebowitz-Speer-Spohn (DLSS) quantum drift diffusion equation, which is the Wasserstein gradient flow of the Fisher information, we study in details solutions of the corresponding implicit Euler scheme. We also take advantage of the convex (but non-smooth) nature of the corresponding variational problem to propose a numerical method based on the Chambolle-Pock primal-dual algorithm.

Author information

Contact details are reproduced from the original publication and may be historical.

Daniel Matthes

Dept. of Mathematics, School of CIT, Technische Universität, München, Germany

matthes@ma.tum.de

Keywords

  • DLSS equation
  • Wasserstein distance
  • Fisher information
  • convex duality
  • Chambolle-Pock algorithm

Mathematics Subject Classification

49Q22, 65K10

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Suggested citation

G. Carlier, J.-D. Benamou, D. Matthes. “Wasserstein Gradient Flow of the Fisher Information from a Non-Smooth Convex Minimization Viewpoint.” Journal of Convex Analysis 31 (2024), No. 2, 359–378. https://doi.org/10.68381/jca31023

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