{"title":"非标准p(x,t)，q(x,t)-增长条件下抛物方程解的正则性和存在性","authors":"Hamid El Bahja","doi":"10.7494/opmath.2023.43.6.759","DOIUrl":null,"url":null,"abstract":"We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard \\(p(x,t),q(x,t)\\)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time \\(L^{\\infty}\\) bounds for the weak solutions.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions\",\"authors\":\"Hamid El Bahja\",\"doi\":\"10.7494/opmath.2023.43.6.759\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard \\\\(p(x,t),q(x,t)\\\\)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time \\\\(L^{\\\\infty}\\\\) bounds for the weak solutions.\",\"PeriodicalId\":45563,\"journal\":{\"name\":\"Opuscula Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Opuscula Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7494/opmath.2023.43.6.759\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Opuscula Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7494/opmath.2023.43.6.759","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions
We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard \(p(x,t),q(x,t)\)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time \(L^{\infty}\) bounds for the weak solutions.
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