{"title":"On the existence of a solution of a class of non-stationary free boundary problems","authors":"M. Bousselsal, A. Lyaghfouri, E. Zaouche","doi":"10.3336/GM.53.2.13","DOIUrl":null,"url":null,"abstract":"We consider a class of parabolic free boundary problems with heterogeneous coefficients including, from a physical point of view, the evolutionary dam problem. We establish existence of a solution for this problem. We use a regularized problem for which we prove existence of a solution by applying the Tychonoff fixed point theorem. Then we pass to the limit to get a solution of our problem. We also give a regularity result of the solutions.","PeriodicalId":55601,"journal":{"name":"Glasnik Matematicki","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasnik Matematicki","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/GM.53.2.13","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
We consider a class of parabolic free boundary problems with heterogeneous coefficients including, from a physical point of view, the evolutionary dam problem. We establish existence of a solution for this problem. We use a regularized problem for which we prove existence of a solution by applying the Tychonoff fixed point theorem. Then we pass to the limit to get a solution of our problem. We also give a regularity result of the solutions.
期刊介绍：
Glasnik Matematicki publishes original research papers from all fields of pure and applied mathematics. The journal is published semiannually, in June and in December.
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