Higher-order robust attractors for stochastic retarded degenerate parabolic equations

Abstract We study the existence, measurability and time-dependent property of pullback random attractors in the higher-order space for stochastic degenerate parabolic equations with variable delay defined on Let X, Z be the square integrable space and the p-times (p > 2) integrable space, respectively. We first prove the existence of a unique pullback -random attractor with and and establish the forward compactness, measurability and long-time stability of the bi-spatial attractor in the higher-order space We then investigate the higher-order delay-free stability of in more precisely, the upper semicontinuity of under the topology of as the memory time tends to zero is established.