Entire Solutions for Bistable Lattice Differential Equations with Obstacles
Dynamical Systems
2013-10-21 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.1310.4978,
title = {Entire Solutions for Bistable Lattice Differential Equations with Obstacles},
author = {A. Hoffman and H. J. Hupkes and E. Van Vleck},
journal= {arXiv preprint arXiv:1310.4978},
year = {2013}
}
Comments
96 pages