Bernadette Miara

Existence theorems for two-dimensional linear shell theories

We consider linearly elastic shells whose middle surfaces have the most general geometries, and we provide complete proofs of the ellipticity of the strain energies found in two commonly used two-dimensional models: Koiters model and Naghdis model.

Boundary Observation and Exact Control of a Quasi-electrostatic Piezoelectric System in Multilayered Media

We study the evolution of a layered quasi-electrostatic piezoelectric system. Under suitable assumptions on the geometry of a region and the interfaces as well as a monotonicity condition on the coefficients, we prove a boundary observation inequality which together with the Hilbert uniqueness method introduced by Lions give us a solution of the exact controllability problem for the model under study.

Exact Controllability of a Koiter Shell by a Boundary Action

We consider a thin shell whose elastic deformations are described by the system of Koiter linear partial differential equations. The shell is controlled by functions acting along its boundary. We show, using the HUM method (Hilbert Uniqueness Method) of J.L. Lions, that when the middle surface of the shell satisfies specific geometrical assumptions, it is possible to obtain exact controllability which consists in driving the system to rest in finite time. In particular we identify the function spaces where the initial Cauchy data (initial displacement and velocity fields) have to be taken and the function space where the control can be chosen in order to get the exact controllability.