Boundary null controllability of degenerate wave equation as the limit of internal controllability

Abstract

This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_{\epsilon },v_{\epsilon }){)}_{\epsilon >0}$, solving related internal null controllability problems. The passage to the limit argument will be rigorously performed through the obtainment of a refined observability type inequality, with a constant explicitly given in terms of $\epsilon >0$. This represents an essential point, since will allow us to achieve our required weak convergence results.