{"title":"Existence results for a class of two-fold saddle point parabolic differential equations","authors":"","doi":"10.1007/s10986-023-09616-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We combine the theory for linear degenerate parabolic problems with results about stationary two-fold saddle point equations to deduce sufficient conditions for the existence and uniqueness of a solution for the problem. Finally, we show some applications of the developed theory through examples that come from <em>fluid dynamic</em> and <em>electromagnetic</em> problems.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lithuanian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10986-023-09616-w","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: 0
Abstract
We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We combine the theory for linear degenerate parabolic problems with results about stationary two-fold saddle point equations to deduce sufficient conditions for the existence and uniqueness of a solution for the problem. Finally, we show some applications of the developed theory through examples that come from fluid dynamic and electromagnetic problems.
期刊介绍：
The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics.
The scope of the journal includes but is not limited to:
Probability theory and statistics;
Differential equations (theory and numerical methods);
Number theory;
Financial and actuarial mathematics, econometrics.
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