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Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations

Abstract:

In this paper we study the existence of one-dimensional travelling wave solutions u(x, t) = φ(x - ct) for the non-linear degenerate (at u = 0) reaction-diffusion equation ut = [D(u)ux]x + g(u) where g is a generalisation of the Nagumo equation arising in nerve conduction theory, as well as describing the Allee effect. We use a dynamical systems approach to prove: 1. the global bifurcation of a heteroclinic cycle (two monotone stationary front solutions), for c = 0, 2. The existence of a uniqu...

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Publication status:
Published

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Publisher copy:
10.1007/s002850050073

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
JOURNAL OF MATHEMATICAL BIOLOGY
Volume:
35
Issue:
6
Pages:
713-728
Publication date:
1997-06-01
DOI:
EISSN:
1432-1416
ISSN:
0303-6812
Source identifiers:
19817
Language:
English
Keywords:
Pubs id:
pubs:19817
UUID:
uuid:6f0e294e-1ce3-48bd-9996-025a864aacca
Local pid:
pubs:19817
Deposit date:
2012-12-19

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