Sufficient Conditions for the Controllability of Wave Equations with a Transmission Condition at the Interface

TL;DR

This paper establishes geometric and propagation speed conditions under which wave equations with transmission conditions at an interface are controllable, extending control theory to complex multi-medium wave systems.

Contribution

It provides new sufficient conditions for boundary controllability of wave equations with transmission conditions at interfaces, considering refraction and geometry effects.

Findings

Derived geometric conditions for controllability

Identified the role of propagation speeds in control feasibility

Extended control results to wave systems with interfaces

Abstract

We consider waves travelling in two different mediums each endowed with a different constant speed of propagation. At the interface between the two mediums, the refraction of the rays of the optic geometry is described by the Snell-Descartes law. We provide sufficient conditions on the geometry of the mediums and on the speed of propagation for the boundary controllability.