Abstract:
Reaction-diffusion equations have a wide range of applications in particular in biology and chemistry and are well known for their ability to reveal patterns and waves. The appearance of a wave in many phenomena is a key element to a development process and a profound understanding of their properties is therefore essential. A classical nonlinear reaction-diffusion equation is the so-called Fisher equation, for which travelling wave solutions connecting two different far-field states are investigated. Their existence proof thereby is based upon phase plane analysis.