A compelling holographic model for the heavy ion collisions and the subsequent evolution of the resulting quark-gluon plasma are the shock wave collisions in AdS space. In this project we present for the first time a fully fledged shock wave collision evolution in a one parameter family of non-conformal theories. The model studied shows a non-trivial RG flow between two fixed points, and its thermodynamics resembles qualitatively ( and for some magnitudes) the one of QCD. The preliminar results show how the relaxation times of the expanding plasma increase with the non-conformality and differ very significantly from the ones computed at a linear level through the quasi-normal modes spectra (which saturate).