{"title":"On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $$\\mathbb{A}{{\\mathbb{T}}_{{\\lambda ,j}}}$$","authors":"A. Yu. Trynin","doi":"10.3103/s1066369x24700105","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper proposes a new method for obtaining a generalized solution to the mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions to the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700105","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The paper proposes a new method for obtaining a generalized solution to the mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions to the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.
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