Propagation failure in the discrete Nagumo equation
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- by H. J. Hupkes, D. Pelinovsky and B. Sandstede PDF
- Proc. Amer. Math. Soc. 139 (2011), 3537-3551 Request permission
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
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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
- MR Author ID: 768528
- Email: hjhupkes@gmail.com
- D. Pelinovsky
- Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
- MR Author ID: 355614
- ORCID: 0000-0001-5812-440X
- Email: dmpeli@math.mcmaster.ca
- B. Sandstede
- Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
- ORCID: 0000-0002-5432-1235
- Email: bjorn_sandstede@brown.edu
- 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
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2813385