  We study the persistence and propagation (or blocking) phenomena for a
species in periodically hostile environments. The problem is described by a
reaction-diffusion equation with zero Dirichlet boundary condition. We first
derive the existence of a minimal nonnegative nontrivial stationary solution
and study the large-time behavior of the solution of the initial boundary value
problem. To the main goal, we then study a sequence of approximated problems in
the whole space with reaction terms which are with very negative growth rates
outside the domain under investigation. Finally, for a given unit vector, by
using the information of the minimal speeds of approximated problems, we
provide a simple geometric condition for the blocking of propagation and we
derive the asymptotic behavior of the approximated pulsating travelling fronts.
Moreover, for the case of constant diffusion matrix, we provide two conditions
for which the limit of approximated minimal speeds is positive.
