Entire Solutions for Bistable Lattice Differential Equations with Obstacles

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Entire Solutions for Bistable Lattice Differential Equations with Obstacles is written by Aaron Hoffman and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 1470422018 (ISBN 10) and 9781470422011 (ISBN 13).

The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by “holes”) are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) 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.