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arXiv · 2606.01812

Uniqueness of an Inverse Coefficient Problem for a Time-Fractional Damped Wave Equation from Boundary Measurements

Kai Yu
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Abstract

This paper studies an inverse coefficient problem for a time-fractional damped wave equation on a finite time interval. The aim is to determine two spatially varying coefficients, namely the fractional damping coefficient and the zeroth-order potential, from the associated Dirichlet-to-Neumann (DtN) map. We first prove the well-posedness of the forward problem for boundary data with sufficient regularity to admit a suitable lifting. The main result is a uniqueness theorem showing that if two coefficient pairs give rise to the same DtN map, then the corresponding coefficients coincide almost everywhere in the domain. The proof is based on a convolution-type integral identity that eliminates the unknown boundary traces, the construction of high-frequency beam solutions adapted to the singular kernel of the Caputo derivative, and a detailed asymptotic analysis of the resulting fractional convolution terms. This result extends classical uniqueness results for hyperbolic inverse problems to a fractional-order model with damping and provides a theoretical basis for related applications involving memory and viscoelastic effects.

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Kai Yu. 2026-06-01. Uniqueness of an Inverse Coefficient Problem for a Time-Fractional Damped Wave Equation from Boundary Measurements. https://arxiv.org/abs/2606.01812

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