{"title":"粗糙路径驱动的传输方程的初始边界值问题","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":"{\"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}","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
摘要
在本文中，我们关注的是由弱几何荷尔德 p p - 通过路径驱动的传输方程的初始 Dirichlet 边界值问题。我们引入了带边界条件的粗糙偏微分方程解的概念。因此，我们将在下文所述的一些假设条件下建立这样一个解的好求解性。此外，我们还将明确给出解。
Initial-boundary value problem for transport equations driven by rough paths
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.
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