{"title":"具有变指数和正则数据的各向异性抛物问题","authors":"Rabah Mecheter","doi":"10.23939/mmc2022.03.519","DOIUrl":null,"url":null,"abstract":"In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces. We prove a \"version\" of a weak Lebesgue space estimate that goes back to \"Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)\" for parabolic equations with anisotropic constant exponents (pi(⋅)=pi).","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Anisotropic parabolic problem with variable exponent and regular data\",\"authors\":\"Rabah Mecheter\",\"doi\":\"10.23939/mmc2022.03.519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces. We prove a \\\"version\\\" of a weak Lebesgue space estimate that goes back to \\\"Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)\\\" for parabolic equations with anisotropic constant exponents (pi(⋅)=pi).\",\"PeriodicalId\":37156,\"journal\":{\"name\":\"Mathematical Modeling and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modeling and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23939/mmc2022.03.519\",\"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":"Mathematical Modeling and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/mmc2022.03.519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了一类具有正则数据的非线性抛物型方程在变指数Sobolev空间中弱解的存在性。我们证明了一个弱Lebesgue空间估计的“版本”,它可以追溯到“Lions J. L. Quelques msamothodes de racimetmes aux limits”。Dunod, Paris(1969)“具有各向异性常数指数(pi(⋅)=pi)的抛物方程”。
Anisotropic parabolic problem with variable exponent and regular data
In this paper, we study the existence of weak solutions for a class of nonlinear parabolic equations with regular data in the setting of variable exponent Sobolev spaces. We prove a "version" of a weak Lebesgue space estimate that goes back to "Lions J. L. Quelques méthodes de résolution des problèmes aux limites. Dunod, Paris (1969)" for parabolic equations with anisotropic constant exponents (pi(⋅)=pi).