{"title":"一类非散度抛物型方程混合问题解趋于零的充分必要条件","authors":"Yu. A. Alkhutov, V. N. Denisov","doi":"10.1090/S0077-1554-2014-00233-8","DOIUrl":null,"url":null,"abstract":"We consider the first boundary value problem in a cylindrical domain for a uniformly parabolic second-order equation in nondivergence form. The solution satisfies the homogeneous Dirichlet condition on the lateral surface of the cylinder, and the initial function is bounded. We show that if the coefficients of the equation satisfy the local and global Dini conditions, then a necessary and sufficient condition for the stabilization of the solution to zero coincides with a similar condition for the heat equation.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"75 1","pages":"233-258"},"PeriodicalIF":0.0000,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00233-8","citationCount":"6","resultStr":"{\"title\":\"Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero\",\"authors\":\"Yu. A. Alkhutov, V. N. Denisov\",\"doi\":\"10.1090/S0077-1554-2014-00233-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the first boundary value problem in a cylindrical domain for a uniformly parabolic second-order equation in nondivergence form. The solution satisfies the homogeneous Dirichlet condition on the lateral surface of the cylinder, and the initial function is bounded. We show that if the coefficients of the equation satisfy the local and global Dini conditions, then a necessary and sufficient condition for the stabilization of the solution to zero coincides with a similar condition for the heat equation.\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"75 1\",\"pages\":\"233-258\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00233-8\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/S0077-1554-2014-00233-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/S0077-1554-2014-00233-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero
We consider the first boundary value problem in a cylindrical domain for a uniformly parabolic second-order equation in nondivergence form. The solution satisfies the homogeneous Dirichlet condition on the lateral surface of the cylinder, and the initial function is bounded. We show that if the coefficients of the equation satisfy the local and global Dini conditions, then a necessary and sufficient condition for the stabilization of the solution to zero coincides with a similar condition for the heat equation.
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