PDE and ODE limit problems for -Laplacian parabolic equations

In this work we prove continuity of solutions with respect to initial conditions and parameters and we prove upper semicontinuity of a family of global attractors for problems of the form u t − div ( D λ | ∇ u λ | p ( x ) − 2 ∇ u λ ) = B ( u λ ) in a bounded smooth domain Ω in R N .