Year: 2025
Type: article
Abstract: We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity properties of the Neumann-to-Dirichlet operator with respect to the material parameters, which provides a theoretical foundation for stable support identification. To improve reconstruction accuracy, particularly when parameters have disjoint supports, we propose a combined regularization approach integrating monotonicity principles with truncated singular value decomposition (TSVD) regularization. This hybrid strategy enhances robustness against noise and ensures sharper support localization. Numerical experiments demonstrate the effectiveness of the proposed method, confirming its applicability in practical scenarios with varying parameter configurations.
DOI: 10.3934/cac.2025023
Authors: Houcine Meftahi, Chayma Nssibi
Institutions: University of Jendouba, Tunis El Manar University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7083446978