Entire solutions for bistable lattice differential equations with obstacles

We consider scalar lattice dierential 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 [9] 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-diusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.