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Article
Multidimensional Stability of Waves Traveling Through Rectangular Lattices in Rational Directions
2012
  • Aaron Hoffman, Franklin W. Olin College of Engineering
  • Hermen Jan Hupkes, University of Leiden
  • Erik S. Van Vleck, University of Kansas Main Campus
Document Type
Article
Publication Date
9-1-2012
Disciplines
Abstract
We consider general reaction di usion 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 di erential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.
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© 2012 Cornell University. This article was published online in September 2012 and can be found here.

Citation Information
Aaron 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/