A partial data coefficient identification inverse problem for a semilinear damped wave operator

Mandeep Kumar; Parveen Kumar; Manmohan Vashisth

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arXiv · 2608.29918

A partial data coefficient identification inverse problem for a semilinear damped wave operator

Mandeep Kumar·Parveen Kumar·Manmohan Vashisth

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Abstract

This manuscript deals with a coefficient identification inverse problem for a semilinear damped wave operator in a bounded domain of $\mathbb{R}^{1+d}\ (d\geq 2)$. We establish the unique recovery of the damping coefficient, zeroth-order linear term, and the coefficient of the power-type nonlinearity from the partial Dirichlet-to-Neumann map. We investigate the corresponding uniqueness problem under the assumption that the coefficients are known in a neighborhood of the boundary, while the Neumann boundary data are prescribed only on an arbitrarily small open subset of the boundary. The analysis is largely based on the unique continuation principle, Fourier Analysis and the higher-order linearization technique.

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Mandeep Kumar, Parveen Kumar, Manmohan Vashisth. 2026-08-30. A partial data coefficient identification inverse problem for a semilinear damped wave operator. https://arxiv.org/abs/2608.29918

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