Exact boundary controllability for wave equations with fixed and moving boundaries in two-dimensional convex-complemented domains

The purpose of this article is to study exact boundary problems for the standard wave equation in domains that are the exterior of a convex compact set of $\mathbb{R}^2$, where both have a common boundary part. We consider two cases: first where the boundary domain is fixed, and where a part of the boundary is moving. In both cases we consider control problems with controls acting only one part of the boundary. For the fixed boundary case the control is of Neumann type, and for the moving boundary case the control is a conormal derivative type. The controllability method used here was developed by Russell [17]. For more information see https://ejde.math.txstate.edu/Volumes/2025/25/abstr.html