{"title":"An efficient heat problem","authors":"T. Burton","doi":"10.7153/dea-2022-14-16","DOIUrl":null,"url":null,"abstract":". By means of fi xed point theory we study properties of solutions of a Volterra integral heat equation by fi mapping it into where is the resolvent of JA , J is a large positive number, and f is bounded. It turns out that the linear part has a unique fi xed point which is a uniformly good approximation of a fi xed point for the non- linear equation.Theobjective is to obtain conditions under which the heat applied by a ( t ) concentrates on the solution x ( t ) .","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2022-14-16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
. By means of fi xed point theory we study properties of solutions of a Volterra integral heat equation by fi mapping it into where is the resolvent of JA , J is a large positive number, and f is bounded. It turns out that the linear part has a unique fi xed point which is a uniformly good approximation of a fi xed point for the non- linear equation.Theobjective is to obtain conditions under which the heat applied by a ( t ) concentrates on the solution x ( t ) .
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