{"title":"The total variation flow in metric graphs","authors":"J. Mazón","doi":"10.3934/mine.2023009","DOIUrl":null,"url":null,"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.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mine.2023009","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 4
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.
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