{"title":"On the Smoothness of the Poisson Potential for Second-Order Parabolic Systems on the Plane","authors":"E. A. Baderko, K. D. Fedorov","doi":"10.1134/s0012266123120042","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the solution of the Cauchy problem in a strip on the plane for a homogeneous\nsecond-order parabolic system. The coefficients of the system satisfy the double Dini condition.\nThe initial function is continuous and bounded along with its first and second derivatives. Using\nthe Poisson potential, the nature of the smoothness of this solution is studied and the\ncorresponding estimates are proved.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266123120042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the solution of the Cauchy problem in a strip on the plane for a homogeneous
second-order parabolic system. The coefficients of the system satisfy the double Dini condition.
The initial function is continuous and bounded along with its first and second derivatives. Using
the Poisson potential, the nature of the smoothness of this solution is studied and the
corresponding estimates are proved.
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