Some integral geometry problems for wave equations
Some integral geometry problems for wave equations
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DOI：
10.1088/1361-6420/ac77b1
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发表时间：
2021-09
期刊：
影响因子：
2.1
通讯作者：
Yiran Wang
中科院分区：
文献类型：
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作者：
Yiran Wang
我们考虑闵可夫斯基时空上的法向双曲算子的柯西问题和源问题，并研究从沿类光测地线的积分确定解的情况。对于柯西问题，我们对瓦西（Vasy）和王（Wang）（2021年《数学物理通讯》384卷，503 - 532页）所得到的稳定确定结果给出了一个新的证明。对于源问题，我们得到了具有类空奇点的源的稳定确定。我们的证明基于对由严格双曲算子的拟基本解构成的光线变换的正规算子的微局部分析。
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 light-like geodesics. For the Cauchy problem, we give a new proof of the stable determination result obtained by Vasy and Wang (2021 Commun. Math. Phys. 384 503–32). 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.