Stability of Pullback Measure Attractors for Stochastic p‐Laplace Equations With Time‐Dependent Delay

ABSTRACT

For the stochastic nonautonomous ‐Laplace equation on an unbounded domian with time‐dependent delay and nonlinear noise, we study its measure dynamics on the history phase space of all continuous functions defined on the delayed interval. We prove the well‐posedness and Feller property, which allow us to prove the existence and continuity of the dual measure process over the space of all probability measures on the history space. We then construct a pullback measure attractor for the dual measure process. We finally establish the upper semicontinuity of the pullback measure attractor when the scaling ratio of the time‐dependent delay goes to zero. It is the first time to apply the idea of Kolmogorov–Riesz compactness criterions in proving the asymptotic tightness.