色散金属域光散射问题的稳定性

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022020

S. Nicaise, C. Scheid

{"title":"色散金属域光散射问题的稳定性","authors":"S. Nicaise, C. Scheid","doi":"10.3934/eect.2022020","DOIUrl":null,"url":null,"abstract":"In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore, we show that it is polynomially stable and that the exponential stability is conditional on the exponential stability of the Maxwell system.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"91 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability properties for a problem of light scattering in a dispersive metallic domain\",\"authors\":\"S. Nicaise, C. Scheid\",\"doi\":\"10.3934/eect.2022020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore, we show that it is polynomially stable and that the exponential stability is conditional on the exponential stability of the Maxwell system.\",\"PeriodicalId\":48833,\"journal\":{\"name\":\"Evolution Equations and Control Theory\",\"volume\":\"91 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolution Equations and Control Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2022020\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022020","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在这项工作中，我们研究了一个PDE系统的适定性和一些稳定性，该系统模拟了光在带孔的金属域中的传播。这个模型考虑了金属的分散特性。它由麦克斯韦方程组和波型系统之间的线性耦合组成。我们证明了该问题在几种边界条件下是适定性的。进一步，我们证明了它是多项式稳定的，并且指数稳定性的条件是麦克斯韦系统的指数稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stability properties for a problem of light scattering in a dispersive metallic domain

In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore, we show that it is polynomially stable and that the exponential stability is conditional on the exponential stability of the Maxwell system.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology