{"title":"A functional inequality and its applications to a class of nonlinear fourth-order parabolic equations","authors":"Xiangsheng Xu","doi":"10.4310/MAA.2016.V23.N2.A3","DOIUrl":null,"url":null,"abstract":"In this article we study the initial-boundary value problem for a family of nonlinear fourth order parabolic equations. The classical quantum drift-diffusion model is a member of the family. Two new existence theorems are established. Our approach is based upon a semi-discretization scheme, which generates a sequence of positive approximate solutions, and a functional inequality of the type","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"55 1","pages":"173-204"},"PeriodicalIF":0.6000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods and applications of analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/MAA.2016.V23.N2.A3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 3
Abstract
In this article we study the initial-boundary value problem for a family of nonlinear fourth order parabolic equations. The classical quantum drift-diffusion model is a member of the family. Two new existence theorems are established. Our approach is based upon a semi-discretization scheme, which generates a sequence of positive approximate solutions, and a functional inequality of the type
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