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Research Article | Open Access

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

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

Keywords

Cauchy problem3D elliptic equationidentical approximation operatorregularization methodconvergence rates
CLC number: 26D15, 31A25, 31B35

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 6732-6744
DOI: 10.3934/math.2025308

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He S. The identical approximation regularization method for the inverse problem to a 3D elliptic equation with variable coefficients. AIMS Mathematics, 2025, 10(3): 6732-6744. https://doi.org/10.3934/math.2025308

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Received: 12 October 2024
Revised: 12 February 2025
Accepted: 26 February 2025
Published: 15 March 2025
©2025 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)