Some integral geometry problems for wave equations
Analysis of PDEs
2022-07-13 v1
Abstract
We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals along null geodesics. For the Cauchy problem, we give a new proof of the stable determination result obtained in Vasy and Wang [12]. For the source problem, we obtain stable determination for sources with space-like singularities. Our proof is based on the microlocal analysis of the normal operator of the light ray transform composed with the parametrix for strictly hyperbolic operators.
Keywords
Cite
@article{arxiv.2109.14446,
title = {Some integral geometry problems for wave equations},
author = {Yiran Wang},
journal= {arXiv preprint arXiv:2109.14446},
year = {2022}
}