Global Existence and Stability in Porous-elasticity with Heat Conduction

The aim of this thesis is to give some results of existence and general decay, as well as providing the reader
with the methods used to study some elastic, thermoelastic and viscous systems, as well as some wave equation
problems with the presence of various dissipation and damping mechanisms under suitable assumptions. We
have used many methods, including: energy method and Lyapunov function.
We divided the thesis into three parts:
In the first part, we study the existence and general decay of solutions for some porous type systems.
As for the second part, we extend the study to other systems, namely Bresse system and Laminate beam.
Finally the third part is concerned with wave equation problems including Kirchhoff's equations, we study
general decay, blow-up and growth of solutions with various dissipation and damping mechanisms under suitable conditions.