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REGULARITY OF random ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

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Acta Mathematica Scientia 2016年第2期36卷 409-427页

作者：赵文强 School of Mathematics and Statistics Chongqing Technology and Business University

We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.

关键词： random dynamical systems stochastic degenerate parabolic equation multiplicative noise random attractors Wiener process

random Attractors of Boussinesq Equations with Multiplicative Noise

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Acta Mathematica Sinica,English Series 2009年第3期25卷 481-490页

作者： Yang Rong LI Bo Ling GUO School of Mathematics and Statistics Southwest China University Chongqing 400715 P. R. China Center for Nonlinear Study Institute of Beijing Applied Physics and Computational Mathematics Beijing 100088 P. R. China

We study the random dynamical system （RDS） generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.

关键词： random dynamical systems random attractor Boussinesq equation white noise Wiener process

The attractor of the stochastic generalized Ginzburg-Landau equation

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Science China Mathematics 2008年第5期51卷 955-964页

作者： GUO BoLing~1 WANG GuoLian~(2+) Li DongLong~3 1 Institute of Applied Physics and Computational Mathematics,P.O.Box 8009,Beijing 100088,China 2 The Graduate School of China Academy of Engineering Physics,P.O.Box 2101,Beijing 100088,China 3 Department of Information and Computer Science,Guangxi University of Technology,Liuzhou 545006,China Institute of Applied Physics and Computational Mathematics Beijing China The Graduate School of China Academy of Engineering Physics Beijing China Department of Information and Computer Science Guangxi University of Technology Liuzhou China

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system. Then we prove the random system possesses a global random attractor in ... 详细信息

关键词： generalized Ginzburg-Landau equation random dynamical systems random attractor 35K05

THE RELATION OF DIMENSION, ENTROPY AND LYAPUNOV EXPONENT IN random CASE

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Analysis in Theory and Applications 2008年第2期24卷 129-138页

作者： Yun Zhao Department of Mathematics Suzhou University Suzhou 215006 P. R. China

We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we prove a formula relating D（μω） to the entropy and Lyapunov exponents of the random system, where D （μω） is dimHμω, dimBμm, or dimBμm.

关键词： Hausdorff dimension random dynamical systems

Dynamics of a Non-Linear Stochastic Viscoelastic Equation with Multiplicative Noise

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Journal of Partial Differential Equations 2019年第4期32卷 304-325页

作者： CARABALLO Tomas PINA Nicolas MUNOZ Jaime Departmento de Ecuaciones Diferenciales y Andlisis Numerico Universidad de SevillaSevillaEspaha Department of Mathematics University of Bio-BtoChile

The well-posedness and stability properties of a stochastic viscoelastic equation with multiplicative noise,Lipschitz and locally Lipschitz nonlinear terms are *** method of Lyapunov functions is used to investigate the asymptotic dynamics when zero is not a solution of the equation by using an appropriate cocycle and random dynamical *** stability of mild solutions is proved in both cases of Lipschitz and locally Lipschitz nonlinear ***,we investigate the existence of a non-trivial stationary solution which is exponentially stable,by using a general random fixed point theorem for general *** this case,the stationary solution is generated by the composition of random variable and Wiener *** addition,the theory of random dynamical system is used to construct another cocycle and prove the existence of a random fixed point exponentially attracting every path.

关键词： Stochastic viscoelastic exponential stability stabilization random dynamical systems attractors

random Attractor for Stochastic Partly Dissipative systems on Unbounded Domains

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Journal of Partial Differential Equations 2015年第1期28卷 47-73页

作者： WANG Zhi DU XianYun College of Applied Mathematics Chengdu university of information technology Chengdu 610225 China.

In this paper, we consider the long time behaviors for the partly dissipative stochastic reaction diffusion equations. The existence of a bounded random absorbing set is firstly discussed for the systems and then an estimate on the solution is derived when the time is sufficiently large. Then, we establish the asymptotic compactness of the solution operator by giving uniform a priori estimates on the tails of solutions when time is large enough. In the last, we finish the proof of existence a pullback ran- dom attractor in L^2 （R^n） × L^2 （R^n）. We also prove the upper semicontinuity of random attractors when the intensity of noise approaches zero. The long time behaviors are discussed to explain the corresponding physical phenomenon.

关键词： Reaction diffusion equation random dynamical systems random attractors asymp- totic compactness Sobolev compact embedding.

Synchronization of Stochastic Two-Layer Geophysical Flows

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Journal of Partial Differential Equations 2011年第1期24卷 15-36页

作者： HAN Yongqian Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China.

In this paper, the two-layer quasigeostrophic flow model under stochastic wind forcing is considered. It is shown that when the layer depth or density differ- ence across the layers tends to zero, the dynamics on both... 详细信息

关键词： Stochastic flow models random dynamical systems synchronization stochasticPDEs geophysical and climate dynamics.