Convergence to Travelling Waves for Solutions of a Class of Semilinear Parabolic Equations

Abstract

In this paper, we investigate the long-time behaviour of the solutions of a class of semilinear parabolic equations in an infinite cylinder. Such equations arise in various fields, such as biology or flame propagation theory. We prove that the solutions whose initial data, together with being increasing along the axis of the cylinder, satisfy certain growth conditions at its ends, will converge exponentially to travelling front solutions.