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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.

Global dissipativity and inertial manifolds for diffusive burgers equations with low-wavenumber instability