  The remnant of SN 1987A is the best-studied object of its kind. The rich
data-set of its thermal and non-thermal emission across the electromagnetic
spectrum poses a unique testbed for the elaboration of particle-acceleration
theory.
  We use 2D simulations of the progenitor's wind to obtain hydro-profiles for
the medium around the supernova explosion. Various cones along prominent
features of the ambient medium are then used in our time-dependent acceleration
code RATPaC to model the evolution of the emission of SN 1987A and compare it
to observational data. We solve for the transport of cosmic rays and the
hydrodynamical flow, in the test-particle limit.The simulation code relies on
1D profiles but the large expansion speed of the young remnant renders lateral
transport unimportant.
  We find that the increase in thermal X-ray emission predates the increase in
the low-energy gamma-ray brightness by several years. The increase of the
gamma-ray brightness at lower energies is followed by a smooth increase at the
highest energies. The gamma-ray spectrum at the highest energies appears soft
during the brightening but hardens as more material in the equatorial ring gets
shocked. The X-ray and gamma-ray brightness remain almost constant once the SNR
blast-wave passed the region of peak-density in the equatorial plane.
