{"title":"Optimal control problem stated in a locally periodic rough domain: a homogenization study","authors":"S. Aiyappan, Giuseppe Cardone, Carmen Perugia","doi":"10.1080/00036811.2023.2265967","DOIUrl":null,"url":null,"abstract":"AbstractWe study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an L2-cost functional constrained by a Poisson problem having a mixed boundary condition: we assume a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part.Keywords: Homogenizationasymptotic analysisperiodic unfoldinglocally periodic boundaryoptimal control2000 Mathematics Subject Classifications: 80M3580M4035B27 AcknowledgementsThe research by G.C. and C.P was supported by project GNAMPA (INDAM) 2023 “Analisi asintotica di problemi al contorno in strutture sottili o rugose”.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"25 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00036811.2023.2265967","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractWe study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an L2-cost functional constrained by a Poisson problem having a mixed boundary condition: we assume a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part.Keywords: Homogenizationasymptotic analysisperiodic unfoldinglocally periodic boundaryoptimal control2000 Mathematics Subject Classifications: 80M3580M4035B27 AcknowledgementsThe research by G.C. and C.P was supported by project GNAMPA (INDAM) 2023 “Analisi asintotica di problemi al contorno in strutture sottili o rugose”.Disclosure statementNo potential conflict of interest was reported by the author(s).
期刊介绍：
Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal
General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.
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