Abstract
We provide a method to study the double stabilities of a pullback random attractor (PRA) generated from a stochastic partial differential equation (PDE) with delays, such a PRA is actually a family of compact random sets Aϱ(t,·), where t is the current time and ϱ is the memory time. We study its longtime stability, which means the attractor semiconverges to a compact set as the current time tends to minus infinity, and also its zero‐memory stability, which means the delayed attractor semiconverges to the nondelayed attractor as the memory time tends to zero. The stochastic nonautonomous p‐Laplacian equation with variable delays on an unbounded domain will be applied to illustrate the method and some suitable assumptions about the nonlinearity and time‐dependent delayed forces can ensure existence, backward compactness, and double stabilities of a PRA.
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