用分数阶Landweber法恢复时空分数阶扩散波方程的空间依赖源

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-07-03 DOI:10.1080/17415977.2020.1815724

S. Jiang, Yujiang Wu

{"title":"用分数阶Landweber法恢复时空分数阶扩散波方程的空间依赖源","authors":"S. Jiang, Yujiang Wu","doi":"10.1080/17415977.2020.1815724","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"990 - 1011"},"PeriodicalIF":1.1000,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1815724","citationCount":"4","resultStr":"{\"title\":\"Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method\",\"authors\":\"S. Jiang, Yujiang Wu\",\"doi\":\"10.1080/17415977.2020.1815724\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.\",\"PeriodicalId\":54926,\"journal\":{\"name\":\"Inverse Problems in Science and Engineering\",\"volume\":\"29 1\",\"pages\":\"990 - 1011\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/17415977.2020.1815724\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Inverse Problems in Science and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/17415977.2020.1815724\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Inverse Problems in Science and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/17415977.2020.1815724","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 4

摘要

在本文中，我们考虑了用分数Landweber方法恢复时间分数扩散波方程的空间相关源的问题。通过使用最终测量数据，将反问题转化为积分方程。我们使用分数Landweber正则化方法来克服不适定性。我们讨论了一个先验正则化参数选择规则和一个后验正则化参数的选择规则，并证明了反问题的条件稳定性和收敛速度。通过对一维和二维四个算例的数值实验，验证了该方法的有效性。

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

Recovering space-dependent source for a time-space fractional diffusion wave equation by fractional Landweber method

In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.

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

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.