Reconstruction of Heat Sources for Parabolic Equations With Wentzell Boundary Conditions

YI Haihong; YANG Liu; TIAN Yu

doi:10.21656/1000-0887.450029

Volume 46 Issue 4

Apr. 2025

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YI Haihong, YANG Liu, TIAN Yu. Reconstruction of Heat Sources for Parabolic Equations With Wentzell Boundary Conditions[J]. Applied Mathematics and Mechanics, 2025, 46(4): 505-518. doi: 10.21656/1000-0887.450029

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Reconstruction of Heat Sources for Parabolic Equations With Wentzell Boundary Conditions

doi: 10.21656/1000-0887.450029

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, P.R.China

Received Date: 2024-02-02
Rev Recd Date: 2024-11-17
Publish Date: 2025-04-01

Abstract

Abstract

The inverse problem of reconstructing spatially related source terms in parabolic heat conduction equations was studied under the Wentzell boundary conditions and with the terminal temperature measurements. This study has important applications in determining the source terms in heat conduction engineering problems, and the difficulty lies in the handling of the Wentzell boundary conditions. Based on the divergence theorem, the boundary conditions were combined with parabolic equations. The extremum principle was proved differently under various boundary conditions. Due to the ill-posedness of the original problem, based on the framework of the optimal control theory, the original problem was optimized, and the existence and necessary conditions for the regularization solution were established. Furthermore, under the validness of the extremum principle, the uniqueness and stability of the regularization solution were proved.
- inverse source problem,
- Wentzell boundary condition,
- optimal control,
- divergence theorem

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References(17)

References

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