Uniform Observability for a Finite Differences Discretization of a Clamped Beam Equation

The aim of this paper is to prove a uniform observability inequality for a finite differences semi-discretization of a clamped beam equation. A discrete multiplier method is employed in order to obtain the uniform observability of the eigenvectors of the matrix driving the semi-discrete system, corresponding to eigenfrequencies smaller than a precise filtering threshold. This result can be generalized to the uniform observability of every filtered solution. Numerical simulations, concerning the dual controllability problem, illustrate the theoretical results.