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Research Article | Open Access

Reconstruction of initial heat distribution via Green function method

Xiaoping Fang1,2,3, Youjun Deng4,5( ), Zaiyun Zhang6
School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha 410205, Hunan, China
Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Changsha 410205, Hunan, China
National Key Laboratory of Data Intelligence and Smart Society, Changsha 410205, Hunan, China
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
School of Mathematics and Computational Science, Hunan University of Science and Technology, Hunan 411201, China
School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan, China
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Abstract

In this paper, layer potential techniques are investigated for solving the thermal diffusion problem. We construct the Green function to get the analytic solution. Moreover, by combining Fourier transform some attractive relation between initial heat distribution and the final observation is obtained. Finally iteration scheme is developed to solve the inverse heat conduction problem and convergence results are presented.

Keywords

linear heat equationanalytic solutionfundamental solutionGreen functioniteration

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Electronic Research Archive
Volume 30 Issue 8,
August 2022
Pages 3071-3086
DOI: 10.3934/era.2022156

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Cite this article:
Fang X, Deng Y, Zhang Z. Reconstruction of initial heat distribution via Green function method. Electronic Research Archive, 2022, 30(8): 3071-3086. https://doi.org/10.3934/era.2022156

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Received: 25 November 2021
Revised: 18 April 2022
Accepted: 19 April 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)