Well-posed pp-laplacian problems with large diffusion

In this work we study the asymptotic behavior of pp-laplacian parabolic problems of the form ut−D△pu+|u|p−2u=B(u)ut−D△pu+|u|p−2u=B(u) in a bounded smooth domain in RnRn and under Neumann boundary conditions when the diffusion coefficient DD becomes large. We prove, under suitable assumptions, that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity.