CONVERGENCE TO TRAVELING WAVES FOR SOLUTIONS OF A CLASS OF SEMILINEARPARABOLIC EQUATIONS

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 prop agation theory. We prove that the solutions whose initial data, togeth er with being increasing along the axis of the cylinder, satisfy certa in growth conditions at its ends, will converge exponentially to trave lling front solutions. (C) 1994 Academic Press, Inc.