{"title":"与三阶方程相关的柯西问题的适定性","authors":"Y. S. Ayala","doi":"10.14738/tmlai.104.12596","DOIUrl":null,"url":null,"abstract":"\n \n \nIn this article we prove that the Cauchy problem associated to third order equation in periodic Sobolev spaces is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we study its generalization to n-th order equation. \n \n \n","PeriodicalId":119801,"journal":{"name":"Transactions on Machine Learning and Artificial Intelligence","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wellposedness of a Cauchy Problem Associated to Third Order Equation\",\"authors\":\"Y. S. Ayala\",\"doi\":\"10.14738/tmlai.104.12596\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n \\n \\nIn this article we prove that the Cauchy problem associated to third order equation in periodic Sobolev spaces is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we study its generalization to n-th order equation. \\n \\n \\n\",\"PeriodicalId\":119801,\"journal\":{\"name\":\"Transactions on Machine Learning and Artificial Intelligence\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Machine Learning and Artificial Intelligence\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14738/tmlai.104.12596\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Machine Learning and Artificial Intelligence","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14738/tmlai.104.12596","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wellposedness of a Cauchy Problem Associated to Third Order Equation
In this article we prove that the Cauchy problem associated to third order equation in periodic Sobolev spaces is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we study its generalization to n-th order equation.
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