Support identification for parameter variations in a PDE system via regularized methods

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.