Boris V. Kapitonov

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.

Simultaneous exact control of piezoelectric systems in multilayered media

This paper considers a pair of transmission problems for the system of piezoelectricity having piecewise constant coefficients. Under suitable monotonicity conditions on the coefficients and certain geometric conditions on the domain and the interfaces where the coefficients have a jump discontinuity, results on simultaneous boundary observation and simultaneous exact control are established.