{"title":"Quasilinear elliptic systems with nonlinear physical data","authors":"Farah Balaadich, E. Azroul","doi":"10.1216/jie.2021.33.427","DOIUrl":null,"url":null,"abstract":"Using the theory of Young measures, we prove the existence of weak solutions to the following quasilinear elliptic system A(u) = f (x)+divσ0(x,u), where A(u) = −divσ(x,u,Du) and f ∈ WLM(Ω;R). This problem corresponds to a diffusion phenomenon with a source f in a moving and dissolving substance, where the motion is described by σ0.","PeriodicalId":50176,"journal":{"name":"Journal of Integral Equations and Applications","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Integral Equations and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jie.2021.33.427","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Using the theory of Young measures, we prove the existence of weak solutions to the following quasilinear elliptic system A(u) = f (x)+divσ0(x,u), where A(u) = −divσ(x,u,Du) and f ∈ WLM(Ω;R). This problem corresponds to a diffusion phenomenon with a source f in a moving and dissolving substance, where the motion is described by σ0.
期刊介绍：
Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications.
The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field.
The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.
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