Rigorous numerics for Kuramoto-Sivashinski PDE

I will describe the method of self-consistent bounds for dissipative PDEs. On the example of Kuramoto-Sivashinski PDE I will explain how to rigorously integrate forward a dissipative PDE and how using topological tools (for example Brouwer Thm) one can obtain the proof (computer assisted, but rigorous) of the existence of periodic orbits.