Inverse boundary value problems for a quasilinear wave equation on Lorentzian manifolds

Abstract: Inverse problems of recovering the metric and nonlinear terms were originated in the work by Kurylev, Lassas, and Uhlmann for the semilinear wave equation $\square_g u(x) + a(x)u^2(x) = f(x)$ in a manifold without boundary. The idea is to use the linearization and the nonlinear interactions of distorted planes waves to produce point source like singularities in an observable set. In this talk, I will discuss the joint work with Gunther Uhlmann which considers the recovery of the metric and the nonlinear term for a quadratic derivative nonlinear wave equation on a Lorentzian manifold with boundary. The main difficulty that we need to handle here is caused by the presence of the boundary. Our work builds on the previous results and I will discuss the methods to overcome these difficulties.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine