<abstract><p>In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between eigenvalue problem model and one Lamé operators with non self-adjoint perturbations, provide quantitative bounds on location point spectrum in terms suitable norms damping coefficient.</p></abstract>

The aim of this work is to obtain optimal-order error estimates for the LQR (Linear-quadratic regulator) problem in a strongly damped 1-D wave equation. We consider a finite element discretization of the system dynamics and a control law constant in the spatial dimension, which is studied in both point and distributed case. To solve the LQR problem, we seek a feedback control which depends on t...

The eigenfrequencies associated to a scalar damped wave equation are known belong band parallel the real axis. Sjöstrand showed that up set of density 0, confined in thinner determined by Birkhoff limits damping term. In this article we show result is still true for vectorial equation. setting Lyapunov exponents cocycle given term play role setting.