Comportement asymptotique des solutions de certains systèmes dynamiques de types : Onde thermoélastique et viscoélastique

Abstract

This thesis is devoted to the study of asymptotic behavior of three type dynamic systems: Wave, thermoelastic and viscoelastic. In the first and second systems, the dissipation is given by a boundary viscoelastic term and the third system being with a distributed damping term. We prove a general decay of the energy of the solution of each system, under certain necessary and suitable assumptions on the resolvent kernels. To obtain these results, we use the multiplier method such as the energy method, the construction of Lyapunov functions and the properties of convex functions.