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arXiv · 2602.04822

Reconstruction of potential and damping coefficients in a semi-linear wave equation

Rahul Bhardwaj·Mandeep Kumar·Manmohan Vashisth
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Abstract

In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear potentials from the associated Dirichlet-to-Neumann map. The analysis is based on a \emph{higher-order linearization} method. As a key step, we establish the existence of suitable asymptotic solutions, crucial for reconstructing the nonlinear potential. In addition, we also provide a detailed study of the corresponding forward problem.

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Rahul Bhardwaj, Mandeep Kumar, Manmohan Vashisth. 2026-02-04. Reconstruction of potential and damping coefficients in a semi-linear wave equation. https://arxiv.org/abs/2602.04822

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