Abstract
We consider a multidimensional monostable reaction-diffusion equation whose nonlinearityinvolves periodic heterogeneity. This serves as a model ofinvasion for a population facing spatial heterogeneities. As a rescaling parameter tends to zero, we prove theconvergence to a limit interface, whose motion is governed by theminimal speed (in each direction) of the underlying pulsatingfronts. This dependance of the speed on the (moving) normaldirection is in contrast with the homogeneous case and makes theanalysis quite involved. Key ingredients are the recentimprovement \cite{A-Gil} of the well-known spreadingproperties \cite{Wein02}, \cite{Ber-Ham-02}, and the solution of a Hamilton-Jacobi equation.