Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Propagation failure in the discrete Nagumo equation


Authors: H. J. Hupkes, D. Pelinovsky and B. Sandstede
Journal: Proc. Amer. Math. Soc. 139 (2011), 3537-3551
MSC (2010): Primary 34A33, 37L60, 34C45
DOI: https://doi.org/10.1090/S0002-9939-2011-10757-3
Published electronically: April 1, 2011
MathSciNet review: 2813385
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We address the classical problem of propagation failure for monotonic fronts of the discrete Nagumo equation. For a special class of nonlinearities that support unpinned ``translationally invariant'' stationary monotonic fronts, we prove that propagation failure cannot occur. Properties of travelling fronts in the discrete Nagumo equation with such special nonlinear functions appear to be similar to those in the continuous Nagumo equation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 34A33, 37L60, 34C45

Retrieve articles in all journals with MSC (2010): 34A33, 37L60, 34C45


Additional Information

H. J. Hupkes
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics, 202 Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65211
Email: hjhupkes@gmail.com

D. Pelinovsky
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Email: dmpeli@math.mcmaster.ca

B. Sandstede
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email: bjorn_sandstede@brown.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10757-3
Keywords: Lattice differential equation, propagation failure, discrete kink, normally hyperbolic invariant manifold
Received by editor(s): May 6, 2010
Received by editor(s) in revised form: August 24, 2010
Published electronically: April 1, 2011
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society