2024-03-28T11:20:31Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692142022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Dynamical systems in the variational formulation of the Fokker-Plank equation by the Wasserstein metricMikami, T.410R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional and the Gibbs-Boltzmann entropy funcĀtional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker-Planck equation and characterize the limit as a solution to a class of variational problems. We also give a simple approach in a one-dimensional case.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69214info:doi/10.14943/83610https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69214/1/pre464.pdfHokkaido University Preprint Series in Mathematics4641521999-07-01engpublisher