Reaction-diffusion equations in periodic media: spreading speeds and spreading sets

RESUMO

We consider solutions of space-periodic reaction-diffusion-advection equations in the whole space R^N, with general unbounded initial support. We show the existence of spreading sets for the solutions at large time, and variational formulas for the spreading speeds. The location of the upper-level sets of a solution with unbounded initial support is estimated in terms of that initial support and the spreading set for the solutions with bounded initial supports. The results hold for the standard classes of Fisher-KPP, ignition, or bistable reactions. The general results apply to the cases of V-shaped and Lambda-shaped initial supports. The proofs rely in particular on upper estimates of what we call retracting solutions.