局部周期粗糙域的最优控制问题:均匀化研究

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-06 DOI:10.1080/00036811.2023.2265967

S. Aiyappan, Giuseppe Cardone, Carmen Perugia

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引用次数: 0

摘要

摘要研究了一类局部周期快速振荡域上的线性最优控制问题的渐近性。我们考虑一个由泊松问题约束的l2代价泛函，它具有混合边界条件:我们在边界的振荡部分假设齐次Neumann条件，在其余部分假设齐次Dirichlet条件。关键词:均匀化，渐近分析，周期展开，局部周期边界，最优控制2000数学学科分类:80M3580M4035B27致谢G.C.和C.P的研究得到了GNAMPA (INDAM) 2023项目“结构sotili - rugose的问题同步分析”的支持。披露声明作者未报告潜在的利益冲突。

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Optimal control problem stated in a locally periodic rough domain: a homogenization study

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).

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

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.