Abstract:
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 joint work with Gunther Uhlmann which considers the recovery of the metric and nonlinear terms for a quadratic derivative nonlinear wave equation on a Lorentzian manifold with boundary. We also consider the recovery of the nonlinearity for a quasilinear wave equation arising in ultrasound imaging. The main difficulty that we need to handle here is caused by the presence of the boundary. I will first overview two related inverse boundary problems for semilinear wave equations considered by Hintz, Uhlmann, and Zhai. Our work builds on these previous results and then I will discuss our methods to overcome the difficulties.