A note on the exact boundary controllability for an imperfect transmission problem

Abstract In this note, we consider a hyperbolic system of equations in domain made up two components. We prescribe homogeneous Dirichlet condition on the exterior boundary and jump displacement proportional to conormal derivatives interface. This last is mathematical interpretation an imperfect apply control external and, by means Hilbert Uniqueness Method, introduced J. L. Lions, study related exact controllability problem. The key point derive observability inequality using so called Lagrange multipliers method, then construct through solution adjoint Eventually, prove lower bound for time which depends geometry domain, coefficients matrix proportionality between