  We present a computer assisted method for proving the existence of globally
attracting fixed points of dissipative PDEs. An application to the viscous
Burgers equation with periodic boundary conditions and a forcing function
constant in time is presented as a case study. We establish the existence of a
locally attracting fixed point by using rigorous numerics techniques. To prove
that the fixed point is, in fact, globally attracting we introduce a technique
relying on a construction of an absorbing set, capturing any sufficiently
regular initial condition after a finite time. Then the absorbing set is
rigorously integrated forward in time to verify that any sufficiently regular
initial condition is in the basin of attraction of the fixed point.
