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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-norm can be found as the solution to a space-time mixed formulation. This first-order framework is particularly interesting from a numerical perspective since it is possible to solve the space-time mixed formulation using only piecewise linear <inline-formula><tex-math id="M2">\begin{document}$ C^0 $\end{document}</tex-math></inline-formula>-finite elements. Numerical simulations illustrate the theoretical results.</p>