  The continuum limit of a recently-proposed model for charge transport in
resonant-tunneling semiconductor superlattices is analyzed. It is described by
a nonlinear hyperbolic integrodifferential equation on a one-dimensional
spatial support, supplemented by shock and entropy conditions. For appropriate
parameter values, a time-periodic solution is found in numerical simulations of
the model. An asymptotic theory shows that the time-periodic solution is due to
recycling and motion of shock waves representing domain walls connecting
regions of the superlattice where the electric field is almost uniform.
