UNIFORM INDIRECT BOUNDARY CONTROLLABILITY OF SEMI-DISCRETE 1-d COUPLED WAVE EQUATIONS

In this paper, we treat the problem of uniform exact boundary controllability for the finite-difference space semi-discretization of the 1-d coupled wave equations with a control acting only in one equation. First, we show how, after filtering the high frequencies of the discrete initial data in an appropriate way, we can construct a sequence of uniformly (with respect to the mesh size) bounded controls. Thus, we prove that the weak limit of the aforementioned sequence is a control for the continuous system. The proof of our results is based on the moment method and on the construction of an explicit biorthogonal sequence.