We present analytical and numerical studies of models of supernova-remnant (SNR) blast waves expanding into uniform media and interacting with a denser cavity wall, in one spatial dimension. We predict the nonthermal emission from such blast waves: synchrotron emission at radio and X-ray energies, and bremsstrahlung, inverse-Compton emission (from cosmic-microwave-background seed photons, ICCMB), and emission from the decay of $pi^0$ mesons produced in inelastic collisions between accelerated ions and thermal gas, at GeV and TeV energies. Accelerated particle spectra are assumed to be power-laws with exponential cutoffs at energies limited by the remnant age or (for electrons, if lower) by radiative losses. We compare the results with those from homogeneous (one-zone) models. Such models give fair representations of the 1-D results for uniform media, but cavity-wall interactions produce effects for which one-zone models are inadequate. We study the time evolution of SNR morphology and emission with time. Strong morphological differences exist between ICCMB and $pi^0$-decay emission, at some stages, the TeV emission can be dominated by the former and the GeV by the latter, resulting in strong energy-dependence of morphology. Integrated gamma-ray spectra show apparent power-laws of slopes that vary with time, but do not indicate the energy distribution of a single population of particles. As observational capabilities at GeV and TeV energies improve, spatial inhomogeneity in SNRs will need to be accounted for.
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