Front propagation in periodic media and some applications

The talk will be devoted to nonlinear propagation of pulsating fronts for reaction-diffusion equations in periodic domains. Such problems involve linear and nonlinear elliptic and parabolic equations with periodic coefficients. It is of interest to study the effects of various phenomena such as diffusion, reaction, advection, as well as the geometry of the domain, on the speed of fronts. Some asymptotics and some applications to a periodic patch model in ecology will be given. This talk is based on some works with H. Berestycki, N. Nadirashvili and L. Roques.