The emergence of travelling waves for reaction-diffusion equations under a co-moving change of coordinates

CDSNS Colloquium
Monday, November 30, 2009 - 11:00
1 hour (actually 50 minutes)
Skiles 269
Consejo Superior de Investigaciones Cientificas Madrid, Spain
We introduce a change of coordinates allowing to capture in a fixed reference frame the profile of travelling wave solutions for nonlinear parabolic equations. For nonlinearities of bistable type the asymptotic travelling wave profile becomes an equilibrium state for the augmented reaction-diffusion equation. In the new equation, the profile of the asymptotic travelling front and its propagation speed emerge simultaneously as time evolves. Several numerical experiments illustrate the effciency of the method.