caa a22 4500 477140637 CHVBK 20180405111731.0 cr unu---uuuuu 170330e19970601xx s 000 0 eng 10.1007/s002850050073 doi (NATIONALLICENCE)springer-10.1007/s002850050073 Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations [Elektronische Daten] [Faustino Sánchez-Garduño, Philip K. Maini] 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 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 φ(x−c * t) is a travelling wave solution of sharp type and 3. A continuum of monotone and oscillatory fronts for c≠c *. We present some numerical simulations of the phase portrait in travelling wave coordinates and on the full partial differential equation. Springer-Verlag Berlin Heidelberg, 1997 Key words: Sharp fronts nationallicence Degenerate diffusion nationallicence Hamiltonian nationallicence Bifurcation of heteroclinic trajectories nationallicence Sánchez-Garduño Faustino Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, C.U., México 04510, D.F., Mexico, MX aut Maini Philip K. Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK, GB aut https://doi.org/10.1007/s002850050073 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002850050073 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sánchez-Garduño Faustino Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, C.U., México 04510, D.F., Mexico, MX aut NATIONALLICENCE 700 1- Maini Philip K. Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, UK, GB aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer