Controllability of the linear elasticity as a first-order system using a stabilized space-time mixed formulation

Abstract

The aim of this paper is to study the boundary controllability of the linear elasticity system as a first-order system in both space and time. Using the observability inequality known for the usual second-order elasticity system, we deduce an equivalent observability inequality for the associated first-order system. Then, the control of minimal \begin{document}$ L^2 $\end{document}-norm can be found as the solution to a space-time mixed formulation. This first-order framework is particularly interesting from a numerical perspective since it is possible to solve the space-time mixed formulation using only piecewise linear \begin{document}$ C^0 $\end{document}-finite elements. Numerical simulations illustrate the theoretical results.