Abstract

We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We obtain a global exact controllability result for this semilinear system with superlinear nonlinearities. For this purpose, we establish an observability estimate for the linearized system with bounded potentials. Moreover, we obtain an explicit estimate of the observability constant in terms of the norms of the potentials. Such an estimate is obtained by a combination of a pointwise estimate, a global Carleman estimate for hyperbolic differential operators and an analysis of the regularity of solutions of a auxiliary optimal control problem. The controllability of the semilinear system is proved using the Hilbert Uniqueness Method (HUM) and a fixed point technique. (C) 2019 Elsevier Inc. All rights reserved.