{"title":"Solvability of an Initial–Boundary Value Problem\nfor a Parabolic Equation with a Time-Nonlocal Term\nin Hölder spaces","authors":"A. S. Fomenko","doi":"10.1134/S1990478924030062","DOIUrl":null,"url":null,"abstract":"<p> We consider an initial–boundary value problem for a semilinear parabolic differential\nequation with a time-nonlocal term. This term contains the integral of the solution over the entire\ntime interval on which the problem is considered. The solvability of the problem in\nHölder classes is proved. The uniqueness of the solution is established under a constraint\non the length of the time interval over which the solution is integrated in the nonlocal term.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"441 - 447"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030062","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We consider an initial–boundary value problem for a semilinear parabolic differential
equation with a time-nonlocal term. This term contains the integral of the solution over the entire
time interval on which the problem is considered. The solvability of the problem in
Hölder classes is proved. The uniqueness of the solution is established under a constraint
on the length of the time interval over which the solution is integrated in the nonlocal term.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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