Entire solutions for bistable lattice differential equations with obstacles
Author(s)
Bibliographic Information
Entire solutions for bistable lattice differential equations with obstacles
（Memoirs of the American Mathematical Society, no. 1188）
American Mathematical Society, c2017
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Note
Includes bibliographical references (p. 117-119)
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Main results
Preliminaries
Spreading speed
Large disturbances
The entire solution
Various limits
Proof of Theorem 2.3
Discussion
Acknowledgments
Bibliography.
by "Nielsen BookData"
