International audienceWe present a systematic phenomenological study focused on the time evolution of the non-thermal radiation – from radio waves to gamma rays – emitted by typical supernova remnants via hadronic and leptonic mechanisms, for two classes of progenitors: thermonuclear and core–collapse. To this aim, we develop a numerical tool designed to model the evolution of the cosmic ray spectrum inside a supernova remnant, and compute the associated multi-wavelength emission. We demonstrate the potential of this tool in the context of future population studies based on large collection of high-energy gamma-ray data. We discuss and explore the relevant parameter space involved in the problem, and focus in particular on their impact on t...