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arXiv · 2603.08888

Linearized Boundary Control Method for Damping Reconstruction in an Acoustic Inverse Boundary Value Problem

Tianyu Yang·Yang Yang
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Abstract

We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping from the linearized Neumann-to-Dirichlet map. When the linearization is at a constant background damping, we derive a reconstructive algorithm with stability estimates based on the boundary control method in dimension $n\geq 1$. The reconstruction algorithm is implemented in one dimension to validate its numerical feasibility. When the linearization is at a non-constant background damping, we establish an increasing stability estimate in the time domain in dimension $n\geq 3$.

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Tianyu Yang, Yang Yang. 2026-03-09. Linearized Boundary Control Method for Damping Reconstruction in an Acoustic Inverse Boundary Value Problem. https://arxiv.org/abs/2603.08888

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