Multidimensional Stability of Waves Traveling Through Rectangular Lattices in Rational Directions

Aaron Hoffman, Franklin W. Olin College of Engineering
Hermen Jan Hupkes, University of Leiden
Erik S. Van Vleck, University of Kansas Main Campus

© 2012 Cornell University. This article was published online in September 2012 and can be found here.

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.