Exact Controllability of a Piezoelectric Body. Theory and Numerical Simulation

We study the exact controllability of a three-dimensional body made of a material whose constitutive law introduces an elasticity-electricity coupling. We show that a coupled elastic-electric control acting on the whole boundary of the body drives the system to rest after time large enough. Two-dimensional numerical experiments suggest that controllability can still be achieved by relaxing this restrictive condition using either both controls on a reduced support or elastic control alone. B. Miara supported by the European project “INTAS, Research Project for South Caucasian Republics 06-1000017-8886”. A. Münch partially supported by grants ANR-05-JC-0182-01 and ANR-07-JC-1832-84.