Multidimensional Stability of Waves Travelling Through Rectangular Lattices in Rational Directions
Analysis of PDEs
2014-10-28 v2 Dynamical Systems
Abstract
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small perturbations. We employ recently developed techniques involving point-wise Green's functions estimates for functional differential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.
Cite
@article{arxiv.1209.6416,
title = {Multidimensional Stability of Waves Travelling Through Rectangular Lattices in Rational Directions},
author = {A. Hoffman and H. J. Hupkes and E. Van Vleck},
journal= {arXiv preprint arXiv:1209.6416},
year = {2014}
}
Comments
42 pages; 2 figures