{"title":"Initial-boundary value problem for transport equations driven by rough paths","authors":"Dai Noboriguchi","doi":"10.1090/tpms/1212","DOIUrl":null,"url":null,"abstract":"In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Hölder \n\n \n p\n p\n \n\n-rough paths. We introduce a notion of solutions to rough partial differential equations with boundary conditions. Consequently, we will establish a well-posedness for such a solution under some assumptions stated below. Moreover, the solution is given explicitly.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1212","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Hölder
p
p
-rough paths. We introduce a notion of solutions to rough partial differential equations with boundary conditions. Consequently, we will establish a well-posedness for such a solution under some assumptions stated below. Moreover, the solution is given explicitly.