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Research Article | Open Access

Unicity of solution for a semi-infinite inverse heat source problem

Zui-Cha Deng, Liu Yang( )
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
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Abstract

A semi-infinite inverse source problem in heat conduction equations is considered, where the source term is assumed to be compactly supported in the region. After introducing a suitable artificial boundary, the semi-infinite problem is transformed into a bounded one and the corresponding exact expression of the boundary condition is derived. Then we rigorously prove the uniqueness of the solution of original problem, together with the stability of the corresponding optimal control solution.

Keywords

semi-infinite domainheat conduction equationinverse source problemuniquenessstability
CLC number: 35R30, 49J20

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 7026-7039
DOI: 10.3934/math.2022391

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Cite this article:
Deng Z-C, Yang L. Unicity of solution for a semi-infinite inverse heat source problem. AIMS Mathematics, 2022, 7(4): 7026-7039. https://doi.org/10.3934/math.2022391

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Received: 23 October 2021
Revised: 03 January 2022
Accepted: 06 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

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