Wavefronts for reaction-diffusion

Abstract

Throughout this chapter we consider only wavefront solutions of reaction-diffusion equations of the form

$$ ut = {\left( {a\left( u \right)} \right)_{xx}} + c\left( u \right) $$

(10.1)

where a and c satisfy Hypothesis 2.1 with ℓ <∞. Since the pioneering work of Fisher [105] and of Kolmogorov, Petrovskii and Piskunov [186], much attention has been paid to the study of such solutions for equations of this class. The goal of this chapter is to show how the correspondence between travelling-wave solutions of equation (1.1) and solutions of the integral equation (1.9) may be invoked to generalize these earlier results. The theorems of Chapter 6 cover the previous results on semi-wavefront solutions of equations of the type (10.1).