{"title":"强拟线性抛物型系统","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":"{\"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}","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}
"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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