具有广义阻抗边界条件的亚扩散方程的反源问题

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-04-01 DOI:10.1016/S0034-4877(24)00025-9

Mansur I. Ismailov, Muhammed Çiçek

{"title":"具有广义阻抗边界条件的亚扩散方程的反源问题","authors":"Mansur I. Ismailov, Muhammed Çiçek","doi":"10.1016/S0034-4877(24)00025-9","DOIUrl":null,"url":null,"abstract":"<div><p>The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION\",\"authors\":\"Mansur I. Ismailov, Muhammed Çiçek\",\"doi\":\"10.1016/S0034-4877(24)00025-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.</p></div>\",\"PeriodicalId\":49630,\"journal\":{\"name\":\"Reports on Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0034487724000259\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000259","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一个具有广义阻抗边界条件的一维时分亚扩散方程的逆问题。该边界条件由施加在边界上的二阶空间微分算子给出。逆问题是根据能量测量确定随时间变化的源参数的问题。逆问题的良好求解性是通过应用谱问题特征函数的傅立叶展开来确定的，该谱问题的边界条件中也包含谱参数、核可能具有对角奇异性的 Volterra 型积分方程以及分数型 Gronwall 不等式。

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

INVERSE SOURCE PROBLEM FOR SUBDIFFUSION EQUATION WITH A GENERALIZED IMPEDANCE BOUNDARY CONDITION

The paper considers an inverse problem for a one-dimensional time-fractional subdiffusion equation with a generalized impedance boundary condition. This boundary condition is given by a second-order spatial differential operator imposed on the boundary. The inverse problem is the problem of determining the time dependent source parameter from the energy measurement. The well-posedness of the inverse problem is established by applying the Fourier expansion in terms of eigenfunctions of a spectral problem which has the spectral parameter also in the boundary condition, Volterra type integral equation with the kernel may have a diagonal singularity and fractional type Gronwall inequality.

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

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.