A PARABOLIC EQUATION OF THE KPP TYPE IN HIGHER DIMENSIONS

The aim of this paper is to study the long-time behaviour of the solut ions of a semilinear parabolic equation in an infinite cylinder, which generalises a well-known one-dimensional model that was first investi gated by Kolmogorov, Petrovskii, and Piskunov (KPP). It is shown that the asymptotic behaviour of the solutions strongly depends on the asym ptotic behaviour of the initial datum at the ends of the cylinder. In particular, the equation admits a continuum of travelling wave solutio ns, each of them stable with regard to adequate perturbations.