Homogenization of pulsating travelling fronts
Mohammad El Smaily · arXiv (Cornell University) · 2009
The goal of this paper is to find the homogenized equation of a heterogenous Fisher-KPP model in a periodic medium. The solutions of this model are pulsating travelling fronts whose speeds are superior to a parametric minimal speed c ∗ L. We first find the homogenized limit of the stationary states which depend on the space variable in many cases. Then, we prove that the pulsating travelling fronts converge to a classical u0: = u0(t,x) of a homogenous reaction-diffusion equation. The homogenized limit u0 is also a travelling front whose minimal speed of propagation is given in terms of the coefficients of the problem.