We propose that the space-time evolution of strongly coupled matter formed by ultra-relativistic heavy ion collisions can be modelled by phenomenological equations involving the energymomentum tensor and conserved currents alone. These equations can describe the late stage of local thermal and chemical equilibration of the matter formed after collisions, and its subsequent transition to hydrodynamic expansion in an unified framework. The full set of equations include local energy, momentum and charge conservation; but also additional equations for evolution of non-equilibrium variables. These equations with precisely determined phenomenological parameters can be obtained by the AdS/CFT correspondence. On the gravity side of this correspondence, for vanishing chemical potentials, these phenomenological equations give all solutions of pure gravity in AdS which have regular future horizons. We also discuss field-theoretic grounds for validity of these phenomenological equations. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.