Boundary Control for a Generalized Wave Equation -- Revisiting Russell's Method of Control

Abstract: In this work we study the exact boundary controllability of a generalized wave equation in a nonsmooth domain with a nontrapping obstacle. In the more general case, this work contemplates the boundary control of a transmission problem admitting several zones of transmission. The result is obtained using the technique developed by David Russell, taking advantage of the local energy decay for the problem, obtained through the Scattering Theory as used by Vodev, combined with a powerful trace Theorem due to Tataru.