Nicolae Cîndea
Université Clermont Auvergne, Clermont-Ferrand, France

The aim of this talk is to present some results concerning the boundary controllability of the linear elasticity system considered 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 $L^2$-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 $C^0$-finite elements. Numerical simulations illustrate the theoretical results.

These results are obtained in a joint work with Arthur Bottois.