Reconstruction of initial heat distribution via Green function method

Xiaoping Fang; Youjun Deng; Zaiyun Zhang; Xiaoping Fang; Youjun Deng; Zaiyun Zhang

doi:10.3934/era.2022156

Electronic Research Archive

2022, Volume 30, Issue 8: 3071-3086. doi: 10.3934/era.2022156

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Reconstruction of initial heat distribution via Green function method

1.
School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha 410205, Hunan, China
2.
Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Changsha 410205, Hunan, China
3.
National Key Laboratory of Data Intelligence and Smart Society, Changsha 410205, Hunan, China
4.
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
5.
School of Mathematics and Computational Science, Hunan University of Science and Technology, Hunan 411201, China
6.
School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan, China

Received: 25 November 2021 Revised: 18 April 2022 Accepted: 19 April 2022 Published: 08 June 2022

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.
- linear heat equation,
- analytic solution,
- fundamental solution,
- Green function,
- iteration
Citation: Xiaoping Fang, Youjun Deng, Zaiyun Zhang. Reconstruction of initial heat distribution via Green function method[J]. Electronic Research Archive, 2022, 30(8): 3071-3086. doi: 10.3934/era.2022156

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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.

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