Simultaneous determination of the space-dependent source and the initial distribution in a heat equation by regularizing Fourier coefficients of the given measurements
type: Item
instance of: scholarly article
title: Simultaneous determination of the space-dependent source and the initial distribution in a heat equation by regularizing Fourier coefficients of the given measurements
zbMATH Open document ID: 1440.35189
DOI: 10.1155/2018/8247584
author: Shufang Qiu
author: Wen Zhang
author: Jianmei Peng
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6992028
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8247584
OpenAlex ID: W2811461037
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description: scientific article; zbMATH DE number 6992028