{"title":"具有非强制边界条件的抛物型微分算子的初边值问题","authors":"A. Polkovnikov","doi":"10.17516/1997-1397-2020-13-5-547-558","DOIUrl":null,"url":null,"abstract":"We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"26 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions\",\"authors\":\"A. Polkovnikov\",\"doi\":\"10.17516/1997-1397-2020-13-5-547-558\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space\",\"PeriodicalId\":43965,\"journal\":{\"name\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2020-13-5-547-558\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University-Mathematics & Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2020-13-5-547-558","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions
We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space
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