English

Graph gradient flows : from discrete to continuum

Analysis of PDEs 2022-11-08 v1

Abstract

This 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.

Keywords

Cite

@article{arxiv.2211.03384,
  title  = {Graph gradient flows : from discrete to continuum},
  author = {Yoshikazu Giga and Yves van Gennip and Jun Okamoto},
  journal= {arXiv preprint arXiv:2211.03384},
  year   = {2022}
}

Comments

86 pages, 1 figure

R2 v1 2026-06-28T05:18:31.823Z