Séance Séminaire

Séminaire ACSIOM

Asymptotic spreading for general heterogeneous Fisher-KPP equations

This talk is devoted to propagation phenomena for general heterogeneous reaction-diffusion equations of the Fisher-KPP type, where the coefficients are only assumed to be uniformly continuous and bounded. We will give sharp estimates on the speed at which the solution "invades" the environment, that is, on the location of its level-sets. These estimates involve a new notion of generalized principal eigenvalues for the linear parabolic operator associated with a linearization of the equation. Our result is optimal when the coefficients are random stationary ergodic, almost periodic, asymptotically almost periodic or constant at infinity in every direction. This is a joint work with H. Berestycki (CAMS-EHESS).