The identical approximation regularization method for the inverse problem to a 3D elliptic equation with variable coefficients

Shangqin He; Shangqin He

doi:10.3934/math.2025308

AIMS Mathematics

2025, Volume 10, Issue 3: 6732-6744. doi: 10.3934/math.2025308

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The identical approximation regularization method for the inverse problem to a 3D elliptic equation with variable coefficients

Shangqin He ^,

School of Mathematics and Information Sciences, North Minzu University, Yinchuan, 750021, China

Received: 12 October 2024 Revised: 12 February 2025 Accepted: 26 February 2025 Published: 25 March 2025
MSC : 26D15, 31A25, 31B35

In this article, the Cauchy problem for a 3D elliptic equation is considered in a cylindrical domain. To regularize the problem, we propose a regularization method named "identical approximation regularization", which does not require complicated calculations. Two identical approximate regularization solutions are compared in the numerical section. The experimental results show that the Dirichlet reconstruction solution is more effective than the others.
- Cauchy problem,
- 3D elliptic equation,
- identical approximation operator,
- regularization method,
- convergence rates
Citation: Shangqin He. The identical approximation regularization method for the inverse problem to a 3D elliptic equation with variable coefficients[J]. AIMS Mathematics, 2025, 10(3): 6732-6744. doi: 10.3934/math.2025308

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Abstract

In this article, the Cauchy problem for a 3D elliptic equation is considered in a cylindrical domain. To regularize the problem, we propose a regularization method named "identical approximation regularization", which does not require complicated calculations. Two identical approximate regularization solutions are compared in the numerical section. The experimental results show that the Dirichlet reconstruction solution is more effective than the others.

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