This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro, C\^indea and M\"unch in SIAM J. Control Optim., 52 (2014) for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing the non-cylindrical support $q$ of the control of minimal $L^2(q)$-norm. In this respect, we prove a uniform observability inequality for a class of domains $q$ satisfying the geometric optic condition. The proof based on the d'Alembert formula relies on arguments from graph theory. Numerical experiments are discussed and highlight the influence of the initial condition on the optimal domains.

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<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>