Entire Solutions For Bistable Lattice Differential Equations With Obstacles

Download or read book Entire Solutions for Bistable Lattice Differential Equations with Obstacles written by Aaron Hoffman and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.