{"title":"Strongly quasilinear parabolic systems","authors":"Farah Balaadich, E. Azroul","doi":"10.24193/subbmath.2023.2.10","DOIUrl":null,"url":null,"abstract":"\"Using the theory of Young measures, we prove the existence of solutions to a strongly quasilinear parabolic system \\[\\frac{\\partial u}{\\partial t}+A(u)=f,\\] where $A(u)=-\\text{div}\\,\\sigma(x,t,u,Du)+\\sigma_0(x,t,u,Du)$, $\\sigma(x,t,u,Du)$ and $\\sigma_0(x,t,u,Du)$ are satisfy some conditions and $f\\in L^{p'}(0,T;W^{-1,p'}(\\Omega;\\R^m))$.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis BabesBolyai Geologia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2023.2.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
"Using the theory of Young measures, we prove the existence of solutions to a strongly quasilinear parabolic system \[\frac{\partial u}{\partial t}+A(u)=f,\] where $A(u)=-\text{div}\,\sigma(x,t,u,Du)+\sigma_0(x,t,u,Du)$, $\sigma(x,t,u,Du)$ and $\sigma_0(x,t,u,Du)$ are satisfy some conditions and $f\in L^{p'}(0,T;W^{-1,p'}(\Omega;\R^m))$."
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