scholarly journals Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift–Hohenberg equation with multiplicative noise

2021 ◽  
Vol 62 (11) ◽  
pp. 111507
Author(s):  
Jintao Wang ◽  
Chunqiu Li ◽  
Lu Yang ◽  
Mo Jia
Keyword(s):  
Invariant Measures ◽  
Multiplicative Noise ◽  
Random Attractors

scholarly journals Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)

2020 ◽  
Vol 4 (1) ◽  
pp. 126-141
Author(s):  
Fadlallah Mustafa Mosa ◽  
◽  
Abdelmajid Ali Dafallah ◽  
Eshag Mohamed Ahmed ◽  
Mohamed Y. A Bakhet ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Attractors

scholarly journals Upper Semicontinuity of Random Attractors for Nonautonomous Stochastic Reversible Selkov System with Multiplicative Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Chunxiao Guo ◽  
Yanfeng Guo ◽  
Xiaohan Li
Keyword(s):  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Main Difficulty ◽  
Asymptotic Compactness ◽  
Random Attractors

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

Random attractors for 3D Benjamin–Bona–Mahony equations derived by a Laplace-multiplier noise

2017 ◽  
Vol 18 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Yangrong Li ◽  
Renhai Wang
Keyword(s):  
Dynamical System ◽  
Multiplicative Noise ◽  
Careful Analysis ◽  
Random Dynamical System ◽  
Stochastic Pde ◽  
Limit Set ◽  
Cutoff Function ◽  
Random System ◽  
Random Attractors ◽  
Bbm Equation

This paper contributes the dynamics for stochastic Benjamin–Bona–Mahony (BBM) equations on an unbounded 3D-channel with a multiplicative noise. An interesting feature is that the noise has a Laplace-operator multiplier, which seems not to appear in any literature for the study of stochastic PDE. After translating the stochastic BBM equation into a random equation and deducing a random dynamical system, we obtain both existence and semi-continuity of random attractors for this random system in the Sobolev space. The convergence of the system can be verified without the lower bound assumption of the nonlinear derivative. The tail-estimate is achieved by using a square of the usual cutoff function and by a careful analysis of the solution’s biquadrate. A spectrum method is also applied to prove the collective limit-set compactness.

scholarly journals Random attractors of the stochastic extended Brusselator system with a multiplicative noise

2020 ◽  
Vol 5 (4) ◽  
pp. 3584-3611
Author(s):  
Chunting Ji ◽  
◽  
Hui Liu ◽  
Jie Xin ◽  
◽  
...  
Keyword(s):  
Multiplicative Noise ◽  
Random Attractors

RANDOM ATTRACTORS FOR SECOND ORDER STOCHASTIC LATTICE DYNAMICAL SYSTEMS WITH MULTIPLICATIVE NOISE IN WEIGHTED SPACES

2012 ◽  
Vol 12 (03) ◽  
pp. 1150024 ◽  
Author(s):  
XIAOYING HAN
Keyword(s):  
Existence And Uniqueness ◽  
Multiplicative Noise ◽  
Sufficient Conditions ◽  
Second Order ◽  
Weighted Spaces ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Absorbing Sets ◽  
Random Attractors ◽  
Multiplicative White Noise

In this paper, we study the asymptotic behavior of solutions of a second order stochastic lattice differential equation with multiplicative white noise in weighted spaces. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors.

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