Inverse Problems for Hyperbolic Equations

TL;DR

This paper surveys inverse problems for hyperbolic equations, including stability estimates and special cases like domains with obstacles and Yang-Mills potentials, highlighting recent advances in the field.

Contribution

It compiles and discusses the author's recent results on inverse hyperbolic problems, including stability estimates and specific geometric configurations.

Findings

Stability estimate for the broken X-ray transform with one convex obstacle in 2D

Analysis of inverse problems with time-dependent and independent coefficients

Results on hyperbolic equations with Yang-Mills potentials

Abstract

We give a survey of author's results on the inverse hyperbolic problems with time-dependent and time-independent coefficients. We consider the case of hyperbolic equations with Yang-Mills potentials and the case of domains with obstacles. In particular, we gave a stability estimate for the broken X-ray transform in the case of one convex obstacle in $\mathbb{R}^2$.