Experimental Study of the HUM Control Operator for Linear Waves

Abstract

We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain $\Omega$ of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin approximation of the optimal control operator of the continuous model, based on the spectral theory of the Laplace operator in $\Omega$. This allows us to obtain surprisingly good illustrations of the main theoretical results available on the controllability of waves and to formulate some questions for future analysis of the optimal control theory of waves.