Abstract
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.
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