Analysis of the periodically fragmented environment model: II - biological invasions and pulsating travelling fronts

This paper is concerned with propagation phenomena for reaction-diffusion equations of the type: u(t) - del (.) (A(x)del u) = f (x, u), x is an element of R-N, where A is a given periodic diffusion matrix field, and f is a given nonlinearity which is periodic in the x-variables. This article is the sequel to [H. Berestycki, F Hamel, L. Roques, Analysis of the periodically fragmented environment model: I-influence of periodic heterogeneous environment on species persistence, Preprint]. The existence of pulsating fronts describing the biological invasion of the uniform 0 state by a heterogeneous state is proved here. A variational characterization of the minimal speed of such pulsating fronts is proved and the dependency of this speed on the heterogeneity of the medium is also analyzed. (c) 2005 Published by Elsevier SAS.