  The domain wall problem of the Peccei-Quinn mechanism can be solved if the
Peccei-Quinn symmetry is explicitly broken by a small amount. Domain walls
decay into axions, which may account for dark matter of the universe. This
scheme is however strongly constrained by overproduction of axions unless the
phase of the explicit breaking term is tuned. We investigate the case where the
universe is matter-dominated around the temperature of the MeV scale and domain
walls decay during this matter dominated epoch. We show how the viable
parameter space is expanded.
