  We study the cosmological evolution of domain walls bounded by strings which
arise naturally in axion models. If we introduce a bias in the potential, walls
become metastable and finally disappear. We perform two dimensional lattice
simulations of domain wall networks and estimate the decay rate of domain
walls. By using the numerical results, we give a constraint for the bias
parameter and the Peccei-Quinn scale. We also discuss the possibility to probe
axion models by direct detection of gravitational waves produced by domain
walls.
