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

Arthur Bottois (1) , Nicolae Cîndea (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 \(L^2\)-norm can be found as the solution to a spacetime 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.

Mots clés: controllability; linear elasticity; first-order system; space-time mixed formulation

Domaines: Optimisation et contrôle [math.OC]

Arthur Bottois, Nicolae Cîndea. Controllability of the linear elasticity as a first-order system using a stabilized space-time mixed formulation. Mathematical Control and Related Fields, In press, ⟨10.3934/mcrf.2022028⟩. ⟨hal-03512656⟩