Global existence and exponential stability for some hyperbolic systems with damping terms

Abstract

In this work we study the existence, the unicity and the stability of the solution of some hyperbolic systems. We start by recalling some basic notions, then we will introduce a one-dimensional nonlinear equation of thermoelasticity with second sound we study the existence, the regularity and the stability of the solution. Then we will see the Timoshenko system where we will distinguish two cases : The one where the propagation is equal and the one where it is not, we will build a Lyapunov functional to study the different forms of stability.