Some integral geometry problems for wave equations

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 null geodesics. For the Cauchy problem, we give a new proof of the stable determination result obtained in Vasy and Wang [12]. 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.

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• On the inverse problem of finding cosmic strings and other topological defects
• The Light Ray transform on Lorentzian manifolds
• Determining a nonlinear hyperbolic system with unknown sources and nonlinearity
• Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds