Continuity of the flows and upper semicontinuity of global attractors for -Laplacian parabolic problems

In this work we prove continuity of solutions with respect to initial conditions and exponent parameters and we prove upper semicontinuity of a family of global attractors for one-dimensional problems of the form ∂ u s ∂ t − ∂ ∂ x ( | ∂ u s ∂ x | p s ( x ) − 2 ∂ u s ∂ x ) = B ( u s ) where B is a globally Lipschitz map, p s ( ⋅ ) → p in L ∞ ( I ) ( I : = ( c , d ) and p > 2 constant ) as s goes to infinity.