On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems

Yejuan Wang

doi:10.3934/dcdsb.2016116

Article Contents

2016, Volume 21, Issue 10: 3669-3708. Doi: 10.3934/dcdsb.2016116

This issue Previous Article Finite-time synchronization of competitive neural networks with mixed delays Next Article The steady state solutions to thermohaline circulation equations

On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems

Yejuan Wang^1,

1.
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000

Received: October 31, 2015

Revised: March 31, 2016

Published: November 2016

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Abstract

In this paper, we first present some conditions for the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems with small perturbations. Then we establish the upper semicontinuity of pullback attractors for nonautonomous and stochastic reaction-diffusion delay equations defined on $\mathbb{R}^n$ with small time delay perturbation for which uniqueness of solutions need not hold. Finally, we prove the existence and upper semicontinuity of pullback attractors for nonautonomous and stochastic nonclassical diffusion equations with polynomial growth nonlinearity of arbitrary order and without the uniqueness of solutions.

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Mathematics Subject Classification: Primary: 34K26, 35K57, 37L55.

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