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Research Article | Open Access

The total variation flow in metric graphs

Departamento de Análisis Matemático, Univ. Valencia, Dr. Moliner 50, 46100 Burjassot, Spain
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Abstract

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.

Keywords

metric graphsfunctions of total variationtotal variation flowthe 1-Laplacianasymptotic behaviour

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Mathematics in Engineering
Volume 5 Issue 1,
February 2023
Pages 1-38
DOI: 10.3934/mine.2023009

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Cite this article:
Mazón JM. The total variation flow in metric graphs. Mathematics in Engineering, 2023, 5(1): 1-38. https://doi.org/10.3934/mine.2023009

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Received: 14 October 2021
Revised: 22 December 2021
Accepted: 22 December 2021
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)