  Supernovae (SNe) with strong interactions with circumstellar material (CSM)
are promising candidate sources of high-energy neutrinos and gamma rays, and
have been suggested as an important contributor to Galactic cosmic rays beyond
1 PeV. Taking into account the shock dissipation by a fast velocity component
of SN ejecta, we present comprehensive calculations of the non-thermal emission
from SNe powered by shock interactions with a dense wind or CSM. Remarkably, we
consider electromagnetic cascades in the radiation zone and subsequent
attenuation in the pre-shock CSM. A new time-dependent phenomenological
prescription provided by this work enables us to calculate gamma-ray, hard
X-ray, radio, and neutrino signals, which originate from cosmic rays
accelerated by the diffusive shock acceleration mechanism. We apply our results
to SN IIn 2010jl and SN Ib/IIn 2014C, for which the model parameters can be
determined from the multi-wavelength data. For SN 2010jl, the more promising
case, by using the the latest Fermi Large Area Telescope (LAT) Pass 8 data
release, we derive new constraints on the cosmic-ray energy fraction,
<0.05-0.1. We also find that the late-time radio data of these interacting SNe
are consistent with our model. Further multi-messenger and multi-wavelength
observations of nearby interacting SNe should give us new insights into the
diffusive shock acceleration in dense environments as well as pre-SN mass-loss
mechanisms.
