Multidimensional Stability of Waves Traveling Through Rectangular Lattices in Rational Directions2012
AbstractWe consider general reaction diusion 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 dierential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.
Citation InformationAaron Hoffman, Hermen Jan Hupkes and Erik S. Van Vleck. "Multidimensional Stability of Waves Traveling Through Rectangular Lattices in Rational Directions" (2012)
Available at: http://works.bepress.com/aaron_hoffman/19/