Semi-linear waves with time-dependent speed and dissipation

The main goal of our thesis is to understand qualitative properties of solutions to the Cauchy problem for the semi-linear wave model with time-dependent speed and dissipation. We greatly benefited from very precise estimates for the corresponding linear problem in order to obtain the global existence (in time) of small data solutions. This reason motivated us to introduce very carefully a complete description for classification of our models: scattering, non-effective, effective, over-damping. We have considered those separately