Open AccessThe total variation flow in metric graphs
Author(s) -
José M. Mazón,
AUTHOR_ID
Publication year - 2022
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2023009
Subject(s) - variation (astronomy) , uniqueness , mathematics , metric (unit) , bounded variation , bounded function , flow (mathematics) , combinatorics , discrete mathematics , mathematical analysis , physics , geometry , operations management , economics , astrophysics
Our aim is to study the total variation flow in metric graphs. First, we define the functions of bounded variation in metric graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness of solutions and that the solutions reach the mean of the initial data in finite time. Moreover, we obtain explicit solutions.