On a partial data inverse problem for the semi-linear wave equation
Analysis of PDEs
2025-11-13 v1
Abstract
We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a Lorentzian manifold with boundary. In particular, we do not impose any geometric or size restrictions on the measurement set. The proof relies on the technique of higher order linearization combined with the construction of Gaussian beams with reflections on the boundary.
Cite
@article{arxiv.2511.08794,
title = {On a partial data inverse problem for the semi-linear wave equation},
author = {Boya Liu and Weinan Wang},
journal= {arXiv preprint arXiv:2511.08794},
year = {2025}
}