  This paper is concerned with the spatial propagation of nonlocal dispersal
equations with bistable or multistable nonlinearity in exterior domains. We
obtain the existence and uniqueness of an entire solution which behaves like a
planar wave front as time goes to negative infinity. In particular, some
disturbances on the profile of the entire solution happen as the entire
solution comes to the interior domain. But the disturbances disappear as the
entire solution is far away from the interior domain. Furthermore, we prove
that the solution can gradually recover its planar wave profile and continue to
propagate in the same direction as time goes to positive infinity for compact
convex interior domain. Our work generalizes the local (Laplace) diffusion
results obtained by Berestycki et al. (2009) to the nonlocal dispersal setting
by using new known Liouville results and Lipschitz continuity of entire
solutions due to Li et al. (2010).
