dc.contributor.author |
Maini, PK |
|
dc.contributor.author |
SánchezGarduno, F |
|
dc.date.accessioned |
2011-01-22T10:27:56Z |
|
dc.date.available |
2011-01-22T10:27:56Z |
|
dc.date.issued |
1997 |
|
dc.identifier.issn |
0303-6812 |
|
dc.identifier.uri |
http://hdl.handle.net/11154/2866 |
|
dc.description.abstract |
In this paper we study the existence of one-dimensional travelling wave solutions u(x, t) = phi(x - ct) for the non-linear degenerate (at u = 0) reaction-diffusion equation u(t) = [D(u)u(x)](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 unique value c > 0 of c for which phi(x - ct) is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts for c not equal c. We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation. |
en_US |
dc.language.iso |
en |
en_US |
dc.title |
Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations |
en_US |
dc.type |
Article |
en_US |
dc.identifier.idprometeo |
2968 |
|
dc.source.novolpages |
35(6):713-728 |
|
dc.subject.wos |
Biology |
|
dc.subject.wos |
Mathematical & Computational Biology |
|
dc.description.index |
WoS: SCI, SSCI o AHCI |
|
dc.subject.keywords |
sharp fronts |
|
dc.subject.keywords |
degenerate diffusion |
|
dc.subject.keywords |
Hamiltonian |
|
dc.subject.keywords |
bifurcation of heteroclinic trajectories |
|
dc.relation.journal |
Journal of Mathematical Biology |
|