Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements

Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements

We consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and o...

Full description

Bibliographic Details
Main Authors: Shufang Qiu, Wen Zhang, Jianmei Peng
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/8247584
id doaj-b2bb2c2f3b044f2195bab15ff080aaf8
record_format Article
spelling doaj-b2bb2c2f3b044f2195bab15ff080aaf82021-07-02T10:30:01ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/82475848247584Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given MeasurementsShufang Qiu0Wen Zhang1Jianmei Peng2School of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaSchool of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaSchool of Science, East China University of Technology, Nanchang, Jiangxi 330013, ChinaWe consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem.http://dx.doi.org/10.1155/2018/8247584
collection DOAJ
language English
format Article
sources DOAJ
author Shufang Qiu
Wen Zhang
Jianmei Peng
spellingShingle Shufang Qiu
Wen Zhang
Jianmei Peng
Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
Advances in Mathematical Physics
author_facet Shufang Qiu
Wen Zhang
Jianmei Peng
author_sort Shufang Qiu
title Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
title_short Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
title_full Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
title_fullStr Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
title_full_unstemmed Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements
title_sort simultaneous determination of the space-dependent source and the initial distribution in a heat equation by regularizing fourier coefficients of the given measurements
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description We consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem.
url http://dx.doi.org/10.1155/2018/8247584
work_keys_str_mv AT shufangqiu simultaneousdeterminationofthespacedependentsourceandtheinitialdistributioninaheatequationbyregularizingfouriercoefficientsofthegivenmeasurements
AT wenzhang simultaneousdeterminationofthespacedependentsourceandtheinitialdistributioninaheatequationbyregularizingfouriercoefficientsofthegivenmeasurements
AT jianmeipeng simultaneousdeterminationofthespacedependentsourceandtheinitialdistributioninaheatequationbyregularizingfouriercoefficientsofthegivenmeasurements
_version_ 1721331930392166400

Similar Items