{"title":"spde的边界重整化","authors":"M'at'e Gerencs'er, Martin Hairer","doi":"10.1080/03605302.2022.2109173","DOIUrl":null,"url":null,"abstract":"Abstract We consider the continuum parabolic Anderson model (PAM) and the dynamical equation on the 3-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for a ‘boundary triviality’ result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Boundary renormalisation of SPDEs\",\"authors\":\"M'at'e Gerencs'er, Martin Hairer\",\"doi\":\"10.1080/03605302.2022.2109173\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the continuum parabolic Anderson model (PAM) and the dynamical equation on the 3-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for a ‘boundary triviality’ result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2021-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/03605302.2022.2109173\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2022.2109173","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Abstract We consider the continuum parabolic Anderson model (PAM) and the dynamical equation on the 3-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for a ‘boundary triviality’ result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.
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