  Global well-posedness, existence of globally absorbing sets and existence of
inertial manifolds is investigated for a class of diffusive Burgers equations.
The class includes diffusive Burgers equation with nontrivial forcing, the
Burgers-Sivashinsky equation and the Quasi-Stedy equation of cellular flames.
The global dissipativity is proven in 2D for periodic boundary conditions. For
the proof of the existence of inertial manifolds, the spectral-gap condition,
which Burgers-type equations do not satisfy in its original form is
circumvented by the Cole-Hopf transform. The procedure is valid in both one and
two space dimensions.
