Semi-infinite travelling waves arising in reaction-diffusion models with a moving boundary

Semi-infinite travelling waves arising in reaction-diffusion models with a moving boundary #

Nabil Fadai

14:10 Tuesday in 4Q04.

Part of the Travelling waves session.

Abstract #

We examine travelling wave solutions arising from reaction-diffusion equations that employ moving-boundary conditions. With only a few assumptions on the reaction-diffusion kinetics, a variety of new semi-infinite travelling waves arise in this model framework. In particular, we show that semi-infinite travelling waves in this model exist over a precise range of wavespeeds and determine the necessary conditions for which semi-infinite travelling waves exist for all positive wavespeeds. Approximate solutions of these travelling waves are obtained by means of small/large wavespeed asymptotic limits, and a family of analytically-obtained travelling waves are presented for specific wavespeeds and reaction-diffusion kinetics.