—In this paper, the robustness to model mismatch of a pre-existing collocated boundary adaptive feedback law is investigated. This control law was originally designed for an anti-damped pure wave Partial Differential Equation (PDE). Actuation and measurements are located at the same boundary. Adaptive terms account for uncertain parameters located at the anti-damped boundary, opposite to the collocated actuation and measurement. By extending and transforming the system state using, in particular, backstepping, this paper establishes that this controller is robust to sufficiently small in-domain damping. Simulations are performed to illustrate the interest of this study to attenuate mechanical vibrations in an oil-drilling context.