{"title":"具有变指数和测量数据的拟线性抛物型问题重归一化解的存在性","authors":"Fairouz Souileh, M. Maouni, K. Slimani","doi":"10.5269/bspm.51207","DOIUrl":null,"url":null,"abstract":"In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is: \nu_{t}-\\text{div}(\\left\\vert \\nabla u\\right\\vert ^{p(x)-2}\\nabla u)+\\lambda\\left\\vert u\\right\\vert ^{p(x)-2}u=\\mu\\text{ } &\\text{in}\\hspace{0.5cm}Q=\\Omega \\times ]0,T[,\\\\u=0 & \\text{on}\\hspace{0.5cm}\\Sigma =\\partial \\Omega \\times ]0,T[, \\\\u(.,0)=u_{0}(.) & \\text{in}\\hspace{0.5cm}\\Omega, \nwhere $ \\lambda>0$ and $ T $ is any positive constant, $ \\mu\\in\\mathcal{M}_{0}(Q) $ is any measure with bounded variation over $ Q=\\Omega \\times ]0,T[ $.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The existence of renormalized solution for quasilinear parabolic problem with variable exponents and measure data\",\"authors\":\"Fairouz Souileh, M. Maouni, K. Slimani\",\"doi\":\"10.5269/bspm.51207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is: \\nu_{t}-\\\\text{div}(\\\\left\\\\vert \\\\nabla u\\\\right\\\\vert ^{p(x)-2}\\\\nabla u)+\\\\lambda\\\\left\\\\vert u\\\\right\\\\vert ^{p(x)-2}u=\\\\mu\\\\text{ } &\\\\text{in}\\\\hspace{0.5cm}Q=\\\\Omega \\\\times ]0,T[,\\\\\\\\u=0 & \\\\text{on}\\\\hspace{0.5cm}\\\\Sigma =\\\\partial \\\\Omega \\\\times ]0,T[, \\\\\\\\u(.,0)=u_{0}(.) & \\\\text{in}\\\\hspace{0.5cm}\\\\Omega, \\nwhere $ \\\\lambda>0$ and $ T $ is any positive constant, $ \\\\mu\\\\in\\\\mathcal{M}_{0}(Q) $ is any measure with bounded variation over $ Q=\\\\Omega \\\\times ]0,T[ $.\",\"PeriodicalId\":44941,\"journal\":{\"name\":\"Boletim Sociedade Paranaense de Matematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boletim Sociedade Paranaense de Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5269/bspm.51207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.51207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The existence of renormalized solution for quasilinear parabolic problem with variable exponents and measure data
In this paper, the study of the existence of a renormalized solution for quasilinear parabolicproblem with variable exponents and measure data. The model is:
u_{t}-\text{div}(\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u)+\lambda\left\vert u\right\vert ^{p(x)-2}u=\mu\text{ } &\text{in}\hspace{0.5cm}Q=\Omega \times ]0,T[,\\u=0 & \text{on}\hspace{0.5cm}\Sigma =\partial \Omega \times ]0,T[, \\u(.,0)=u_{0}(.) & \text{in}\hspace{0.5cm}\Omega,
where $ \lambda>0$ and $ T $ is any positive constant, $ \mu\in\mathcal{M}_{0}(Q) $ is any measure with bounded variation over $ Q=\Omega \times ]0,T[ $.