Existence and Exponential Decay for a Contact Problem Between Two Dissipative Beams

Abstract

We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is that we can take advantage of stabilization results of others linear dynamic systems with different dissipative mechanisms and apply them through our method for Contact Problems (see Sect. 4). Finally, thanks to Lipschitzian perturbations we can generalize the Signorini problem to more general semi linear problems in a simple way (see Sect. 4.3).