Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-08-29 DOI:10.1002/mma.10435
A. Kirsch, B. Schweizer
{"title":"Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions","authors":"A. Kirsch, B. Schweizer","doi":"10.1002/mma.10435","DOIUrl":null,"url":null,"abstract":"We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self‐contained exposition. In this context, we simplify the non‐degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/mma.10435","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0

Abstract

We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self‐contained exposition. In this context, we simplify the non‐degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
再论周期波导:辐射条件、极限吸收原理和有界解空间
我们研究了封闭波导中具有周期性系数的亥姆霍兹方程。我们采用函数解析法,在自足的论述中提出并解决了辐射问题。在此背景下,我们简化了频率的非退化假设。我们研究了极限吸收原理(LAPs),并推导出与所选 LAPs 相对应的辐射条件;我们通过一个例子来说明不同的 LAPs 一般会导致辐射问题的不同解决方案。最后,我们描述了同质问题所有有界解的集合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
期刊最新文献
A Systematic Review of Sleep Disturbance in Idiopathic Intracranial Hypertension. Advancing Patient Education in Idiopathic Intracranial Hypertension: The Promise of Large Language Models. Anti-Myelin-Associated Glycoprotein Neuropathy: Recent Developments. Approach to Managing the Initial Presentation of Multiple Sclerosis: A Worldwide Practice Survey. Association Between LACE+ Index Risk Category and 90-Day Mortality After Stroke.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1