Determining Lorentzian manifold from non-linear wave observation at a single point
Analysis of PDEs
2023-10-12 v1
Abstract
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.
Cite
@article{arxiv.2310.06925,
title = {Determining Lorentzian manifold from non-linear wave observation at a single point},
author = {Medet Nursultanov and Lauri Oksanen and Leo Tzou},
journal= {arXiv preprint arXiv:2310.06925},
year = {2023}
}