{"title":"有界域中的非稳态中子输运方程的扩散极限","authors":"Zhimeng Ouyang","doi":"10.1007/s10955-024-03291-y","DOIUrl":null,"url":null,"abstract":"<p>The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with the in-flow, diffuse-reflection, or specular-reflection boundary condition. Using a novel kernel estimate, we demonstrate the optimal <span>\\(L^2\\)</span> diffusive limit in the presence of both initial and boundary layers. Previously, this result was only proved for convex domains when the time variable is involved. Our approach is highly robust, making it applicable to all basic types of physical boundary conditions.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diffusive Limit of the Unsteady Neutron Transport Equation in Bounded Domains\",\"authors\":\"Zhimeng Ouyang\",\"doi\":\"10.1007/s10955-024-03291-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with the in-flow, diffuse-reflection, or specular-reflection boundary condition. Using a novel kernel estimate, we demonstrate the optimal <span>\\\\(L^2\\\\)</span> diffusive limit in the presence of both initial and boundary layers. Previously, this result was only proved for convex domains when the time variable is involved. Our approach is highly robust, making it applicable to all basic types of physical boundary conditions.</p>\",\"PeriodicalId\":667,\"journal\":{\"name\":\"Journal of Statistical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10955-024-03291-y\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10955-024-03291-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Diffusive Limit of the Unsteady Neutron Transport Equation in Bounded Domains
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with the in-flow, diffuse-reflection, or specular-reflection boundary condition. Using a novel kernel estimate, we demonstrate the optimal \(L^2\) diffusive limit in the presence of both initial and boundary layers. Previously, this result was only proved for convex domains when the time variable is involved. Our approach is highly robust, making it applicable to all basic types of physical boundary conditions.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.