{"title":"一类退化抛物型Kolmogorov方程","authors":"M. D. Francesco, A. Pascucci","doi":"10.1155/AMRX.2005.77","DOIUrl":null,"url":null,"abstract":"We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"30 1","pages":"77-116"},"PeriodicalIF":0.0000,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"99","resultStr":"{\"title\":\"On a class of degenerate parabolic equations of Kolmogorov type\",\"authors\":\"M. D. Francesco, A. Pascucci\",\"doi\":\"10.1155/AMRX.2005.77\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.\",\"PeriodicalId\":89656,\"journal\":{\"name\":\"Applied mathematics research express : AMRX\",\"volume\":\"30 1\",\"pages\":\"77-116\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"99\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied mathematics research express : AMRX\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/AMRX.2005.77\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied mathematics research express : AMRX","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/AMRX.2005.77","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a class of degenerate parabolic equations of Kolmogorov type
We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
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