On the stability analysis of boundary conditions for the wave equation by energy methods. part i: The homogeneous case

We reconsider the stability theory of boundary conditions for the wave equation from the point of view of energy techniques. We study, for the case of the homogeneous half-space, a large class of boundary conditions including the so-called absorbing conditions. We show that the results of strong stability in the sense of Kreiss, studied from the point of view of the modal analysis by Trefethen and Halpern, always correspond to the decay in time of a particular energy. This result leads to the derivation of new estimates for the solution of the associated mixed problem.