Varying the direction of propagation in reaction-diffusion equations in periodic media

International audienceWe consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of thepropagation phenomena on the direction. We prove that the(minimal) speed of the underlying pulsating fronts dependscontinuously on the direction of propagation, and so does itsassociated profile provided it is unique up to time shifts. Wealso prove that the spreading properties \cite{Wein02} areactually uniform with respect to thedirection