2024-03-28T22:00:48Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/869782022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Graph gradient flows : from discrete to continuumGiga, YoshikazuGennip, Yves vanOkamoto, Jun410This paper gives a framework to study a continuum limit of a gradient flow on a graph where the number of vertices increases in an appropriate way. As examples we prove the convergence of a discrete total variation flow and a discrete Allen-Cahn flow on discretised tori to their respective continuum limits.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/86978info:doi/10.14943/104493https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/86978/1/Graph_gradient_flows%2020221017.pdfHokkaido University Preprint Series in Mathematics11471862022-10-18engpublisher