Some integral geometry problems for wave equations. (1st August 2022)

• Record Type: Journal Article
• Authors: Wang, Yiran
• Is Part Of: Inverse problems. Volume 38:Number 8(2022)
• Publication Date: 2022-08-01
• Subjects: light ray transform -- wave equation -- microlocal analysis; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac77b1
• Languages: English
• ISSNs: 0266-5611

Abstract

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 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.