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Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide

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arxiv 2409.01913 v1 pith:LP4LN4JT submitted 2024-09-03 math.AP

Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide

Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth This is my paper
classification math.AP
keywords equationmatrixpotentialtime-dependentwavedeterminationgiveninput-output
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We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is given by the input-output map associated with the wave equation. Considering a suitable geometric optics solution and with the help of light ray transform, we demonstrate the stability estimate in the determination of the time-dependent matrix potential from the given input-output map.

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