Stability of an inverse problem for a semi-linear wave equation

Abstract: Stability of an inverse problem deals with the question about whether small errors in the measurement lead only to small errors in the reconstruction. I will discuss the stability and unique recovery of a potential function in a semi-linear wave equation. The inverse problem is formulated on a Lorentzian manifold. Using the nonlinearity of the wave equation, we show that the potential function can be recovered in a H\"older stable way from the Dirichlet-to-Neumann map. This talk is based on a joint work with Matti Lassas, Tony Liimatainen and Leyter Potenciano-Machado.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine