  We consider scalar lattice differential equations posed on square lattices in
two space dimensions. Under certain natural conditions we show that wave-like
solutions exist when obstacles (characterized by "holes") are present in the
lattice. Our work generalizes to the discrete spatial setting the results
obtained in a paper of Berestycki, Hamel and Matano for the propagation of
waves around obstacles in continuous spatial domains. The analysis hinges upon
the development of sub and super-solutions for a class of discrete bistable
reaction-diffusion problems and on a generalization of a classical result due
to Aronson and Weinberger that concerns the spreading of localized
disturbances.
