Double stabilities of pullback random attractors for stochastic delayed p-Laplacian equations |
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Authors: | Qiangheng Zhang Yangrong Li |
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Institution: | School of Mathematics and Statistics, Southwest University, Chongqing, China |
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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 A?(t,·), where t is the current time and ? 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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Keywords: | delayed equations double stability random dynamical systems pullback random attractors stochastic partial differential equations stochastic partial differential equations stochastic p-Laplacian equations |
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