Stabilization of some hyperbolic type problems by boundary controls

Abstract

The aim of this work is to study some systems consisting of partial differential equations. The first problem is the Timoshenko system, we will prove the existence and the uniqueness of the solution based on Faedo-Galerkin method, and the study of its stability is done using the multiplier technique which is based on constructing the Lyapunov function. The second system is that we will study a problem related to machanics specifically elastic materials with voids . First, we prove that the problem has a solution by controlling the boundaries, then we will study the exponential stability of the solution (the study was not completed).