Optimal Internal Stabilization of the Linear System of Elasticity
2009 - A. Muench, P. Pedregal, F. Peragio
Archive Rational Mechanics and Analysis 193, 171-193 (2009)
Pedregal Tercero, Pablo.
We address the non-linear optimal design problem which consists in finding the best position and shape of a feedback damping mechanism for the stabilization of the linear system of elasticity. Non-existence of classical designs are related to the over-damping phenomenon. Therefore, by means of Young measures, a relaxation of the original problem is proposed. Due to the vector character of the elasticity system, the relaxation is carried out through div-curl Young measures which let the analysis be direct and the dimension independent. Finally, the relaxed problem is solved numerically, and a penalization technique to recover quasi-optimal classical designs from the relaxed ones is implemented in several numerical experiments.