Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide
Analysis of PDEs
2024-09-04 v1
Abstract
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.
Cite
@article{arxiv.2409.01913,
title = {Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide},
author = {Nitesh Kumar and Tanmay Sarkar and Manmohan Vashisth},
journal= {arXiv preprint arXiv:2409.01913},
year = {2024}
}