Pullback measure attractors for stochastic p-Laplacian parabolic equations on thin domains

We investigate the pullback measure attractors for non-autonomous stochastic p -Laplacian equations driven by nonlinear noise on thin domains. The concept of complete orbits for such systems is presented to establish the structures of pullback measure attractors. We first present some essential uniform estimates, as well as the existence and uniqueness of pullback measure attractors. A novel technical proof method is shown to overcome the difficulty of the estimates of the solutions in W1,p on thin domains. Then, we prove the upper semicontinuity of these measure attractors as the $(n + 1)$ -dimensional thin domains collapse onto the lower n -dimensional space.