{"title":"变指数齐次Neumann边界条件下非线性抛物型问题的熵解","authors":"U. Traoré","doi":"10.4067/s0719-06462021000300385","DOIUrl":null,"url":null,"abstract":"In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in L 1 . By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents\",\"authors\":\"U. Traoré\",\"doi\":\"10.4067/s0719-06462021000300385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in L 1 . By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.\",\"PeriodicalId\":36416,\"journal\":{\"name\":\"Cubo\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cubo\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4067/s0719-06462021000300385\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cubo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4067/s0719-06462021000300385","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents
In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in L 1 . By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.
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