从波方程解的光锥迹恢复初值
偏微分方程分析
2018-05-23 v2
摘要
我们考虑从光锥上的迹恢复波方程初值问题解的初值的问题。当空间为奇数维时,我们证明从初值到光锥上(关于时间偶或奇)解的迹的映射是一个等距映射,并且刻画了该映射的值域并构造了其逆映射。我们通过将问题与从一个函数关于所有过原点的球面的球均值恢复该函数相联系来做到这一点,而后者又通过R^n上的反演映射与Radon变换反演相关。
引用
@article{arxiv.1801.08818,
title = {Recovering initial values from light cone traces of solutions of the wave equation},
author = {Rakesh and Tao Yuan},
journal= {arXiv preprint arXiv:1801.08818},
year = {2018}
}
备注
This is a revision of an earlier version. The title has been changed (at the request of a referee), constants have been corrected in the formulas in Theorem 3, the formula in Theorem 4 has been corrected and there are corresponding minor changes in the proofs. Sections 1.2 and 1.3 have been swapped and the abstract is a little longer