Exponential Stability in Thermoelastic Timoshenko and Bresse Systems

Abstract

In this thesis we considered some elastic, thermoelastic and viscoelastic systems with the presence of different mechanisms of dissipation damping and for more general forms of nonlinearities addressed from a different angle, and under assumptions on initial data and boundary conditions, conditions on damping and source terms. In our study, we focused on studying the stability of the solution and the instability of the solution (the explosion of the solution at a finite instant in time), and it started with study the existence and uniqueness of the solution we have demonstrated the existence and uniqueness of the solution by using the Semi-group method if the problems studied are linear, and if the problems studied are not linear we applied the Feado-Glarken method.