动力学方程的一个Integral Geometry问题及其反问题的唯一性
Uniqueness in an Integral Geometry Problem and an Inverse Problem for the Kinetic Equation
摘要：
本文讨论了强凸区域上一类积分几何问题的唯一性。我们的问题涉及到由所有边界点对之间的距离求黎曼度量的问题。为了证明该定理，首先将问题归结为黎曼流形上动力学方程的源反问题，然后利用傅里叶分析的工具在半测地坐标下证明了唯一性定理.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
