  We 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 the maximum energy of
accelerated particles, in order to study the effectiveness and duration of the
PeVatron phase. We outline the crucial role of the ambient medium through which
the shock propagates during the remnant evolution. In particular, we point out
the role of dense clumps in creating a significant hardening in the hadronic
gamma-ray spectrum.
