UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR MULTI-VALUED RANDOM COCYCLE

Ting Li

doi:10.11948/20190050

2019 Volume 9 Issue 5

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Ting Li. UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR MULTI-VALUED RANDOM COCYCLE[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1948-1958. doi: 10.11948/20190050

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Ting Li. UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR MULTI-VALUED RANDOM COCYCLE[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1948-1958. doi: 10.11948/20190050

UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR MULTI-VALUED RANDOM COCYCLE

Ting Li^,

School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China

Corresponding author: Li Ting, E-mail: liting@suda.edu.cn
Fund Project: The author was supported by National Natural Science Foundation of China (11771317)

Abstract

Abstract

In this paper we study the upper semicontinuity of random attractors for multi-valued random cocycle when small random perturbations approach zero or small perturbation for random cocycle is considered. Furthermore, we consider the upper semicontinuity of random attractors for multivalued random cocycle under the condition which the metric dynamical systems is ergodic.
- Pullback attractor /
- ergodicity /
- upper semicontinuity
MSC: 37D35, 34D20

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References

[1]	V. P. Bongolan-Walsh, D. Cheban and J. Duan, Recurrent Motions in the Nonautonomous Navier-Stokes System, Discrete and Continuous Dyn. Sys. B, 2002, 3, 255-262. Google Scholar
[2]	T. Caraballo, P. E. Kloeden and J. Real, Pullback and forward attractors for a damped wave equation with delays, Stochastics & Dynamics, 2004, 4(3), 405-423. Google Scholar
[3]	T. Caraballo, J. Langa, V. Melnik and J. Valero, Pullback Attractors of Nonautonomous and Stochastic Multivalued Dynamical Systems, Set-Valued Analysis, 2003, 11, 153-201. doi: 10.1023/A:1022902802385 CrossRef Google Scholar
[4]	T. Caraballo, J. Langa and J. Robinson, Upper semicontinuity of attractors for small random perturbations of dynamical systems, Communications in Partial Differential Equations, 1998, 23(9-10), 1557-1581. doi: 10.1080/03605309808821394 CrossRef Google Scholar
[5]	T. Caraballo, P. Marin-Rubio and J. Valero, Autonomous and non-autonomous attractors for differ- ential equations with delays, J. Differential Equations, 2005, 208, 9-41. doi: 10.1016/j.jde.2003.09.008 CrossRef Google Scholar
[6]	H. Crauel, A. Debussche and F. Flandoli, Random attractors, J. Dyn. Diff. Eq., 1995, 9(2), 307-341. Google Scholar
[7]	H. Crauel and F. Flandoli, Attractors for random dynaniical systems, Probability Theory and Related Fields, 1994, 100(3), 365-393. doi: 10.1007/BF01193705 CrossRef Google Scholar
[8]	P. E. Kloeden and B. Schmalfuss, Asymptotic behaviour of non-autonomous difference inclusions, Systems Control Lett. 1998, 33(4), 275-280. doi: 10.1016/S0167-6911(97)00107-2 CrossRef Google Scholar
[9]	J. A. Langa and B. Schmalfuss, Finite dimensionality of attractors for non-autonomous dynamical systems given by partial differential equations, Stochastics and Dynamics, 2004, 4(3), 385-404. doi: 10.1142/S0219493704001127 CrossRef Google Scholar
[10]	D. S. Li and P. E. Kloeden, On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions, J. Differential Equations, 2006, 224(1), 10-38. Google Scholar
[11]	D. S. Li, Y. J. Wang and S. Y. Wang, On the dynamics of non-autonomous general dynam- ical systems and differential inclusions, Set-Valued Analysis, 2008, 16(5-6), 651-671. doi: 10.1007/s11228-007-0054-8 CrossRef Google Scholar
[12]	T. Li, Pullback attractors for asymptotically upper semicompact non-autonomous multi-valued semiflows, Commun. Pure Appl. Anal., 2007, 6(1), 279-285. Google Scholar
[13]	B. Schmalfuss, Attractors for non-autonomous dynamical systems, in Proc. Equadi 99, Berlin, Eds. B. Fiedler, K. Greger and J. Sprekels (World Scientific, 2000), 684-689. Google Scholar
[14]	P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, NewYork, 1982. Google Scholar
[15]	B. X. Wang, Upper semicontinuity of random attractors for non-compact random dynamical systems, Electron. J. Differ. Equ., 2009, 139, 1-18. Google Scholar
[16]	B. X. Wang, Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms, Stoch. Dyn., 2014, 14(4), 145009. Google Scholar
[17]	J. Y. Wang, Y. J. Wang and D. Zhao, Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays, Stoch. Dyn., 2016, 16(5), 1750001. doi: 10.1142/S0219493717500010 CrossRef Google Scholar
[18]	Y. J. Wang, On the upper semicontinuity of pullback attractors for multi-valued processes, Quarterly of Applied Mathematics, 2013, 71(2), 369-399. doi: 10.1090/S0033-569X-2013-01306-1 CrossRef Google Scholar
[19]	Y. J. Wang, On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems, Discrete and Continuous Dynamical Systems Series B, 2016, 21(10), 3669-3708. doi: 10.3934/dcdsb.2016116 CrossRef Google Scholar
[20]	Y. J. Wang and J. Y. Wang, Pullback attractors for multi-valued non-compact random dynamical systems generated by reaction-diffusion equations on an unbounded domain, J. Differential Equations, 2015, 259(2), 728-776. doi: 10.1016/j.jde.2015.02.026 CrossRef Google Scholar