{"title":"On approximating initial data in some linear evolutionary equations involving fraction Laplacian","authors":"R. Karki","doi":"10.5206/mase/13511","DOIUrl":null,"url":null,"abstract":"We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy. ","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/13511","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy.