Uniqueness in an Integral Geometry Problem and an Inverse Problem for the Kinetic Equation
Differential Geometry
2015-07-28 v2
Abstract
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation on a Riemannian manifold and then the uniqueness theorem is proved in semi-geodesic coordinates by using the tools of Fourier analysis.
Cite
@article{arxiv.1502.05152,
title = {Uniqueness in an Integral Geometry Problem and an Inverse Problem for the Kinetic Equation},
author = {Arif Amirov and Fikret Gölgeleyen and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:1502.05152},
year = {2015}
}
Comments
29 pages. arXiv admin note: text overlap with arXiv:1109.0505 by other authors