On the parabolic equation with the nonlinear Laplacian

We consider a nonlinear evolution equation of parabolic type
having the p-Laplacian as leading operator.
Under very general conditions on the nonlinearity,
we prove the existence of a regular global attractor.
When the nonlinearity is monotone, and in absence of external source terms,
we give an explicit estimate of the decay rate to zero
of the solution.