Citation: |
[1] |
C. T. Anh and N. D. Toan, Existence and upper semicontinuity of uniform attractors in $H^1(\mathbbR^N)$ for nonautonomous nonclassical diffusion equations, Ann. Polon. Math., 111 (2014), 271-295.doi: 10.4064/ap111-3-5. |
[2] |
L. Arnold, Random Dynamical Systems, Springer-Verlag, New York, Berlin, 1998.doi: 10.1007/978-3-662-12878-7. |
[3] |
J. P. Aubin and H. Franskowska, Set-Valued Analysis, Birkhäuser, Bosten, Basel, Berlin, 1990. |
[4] |
P. W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction-diffusion equations on unbounded domains, J. Differ. Equ., 246 (2009), 845-869.doi: 10.1016/j.jde.2008.05.017. |
[5] |
T. Caraballo, J. A. Langa, V. S. Melnik and J. Valero, Pullback attractors of nonautonomous and stochastic multivalued dynamical systems, Set-Valued Anal., 11 (2003), 153-201.doi: 10.1023/A:1022902802385. |
[6] |
T. Caraballo and J. A. Langa, On the upper semicontinuity of cocycle attractors for non-autonomous and random dynamical systems, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 10 (2003), 491-513. |
[7] |
T. Caraballo, M. J. Garrido-Atienza, B. Schmalfuss and J. Valero, Non-autonomous and random attractors for delay random semilinear equations without uniqueness, Discrete Contin. Dyn. Syst., 21 (2008), 415-443.doi: 10.3934/dcds.2008.21.415. |
[8] |
T. Caraballo, M. J. Garrido-Atienza, B. Schmalfuß and J. Valero, Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions, Discrete Contin. Dyn. Syst., 14 (2010), 439-455.doi: 10.3934/dcdsb.2010.14.439. |
[9] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, RI, 2002. |
[10] |
I. D. Chueshov, Monotone Random Systems Theory and Applications, Springer-Verlag, New York, 2002.doi: 10.1007/b83277. |
[11] |
M. Coti Zelati, On the theory of global attractors and Lyapunov functionals, Set-Valued Var. Anal., 21 (2013), 127-149.doi: 10.1007/s11228-012-0215-2. |
[12] |
M. Coti Zelati and P. Kalita, Minimality properties of set-valued processes and their pullback attractors, SIAM J. Math. Anal., 47 (2015), 1530-1561.doi: 10.1137/140978995. |
[13] |
H. Crauel, A. Debussche and F. Flandoli, Random attractors, J. Dynam. Differ. Equ., 9 (1997), 307-341.doi: 10.1007/BF02219225. |
[14] |
K. Deimling, Multivalued Differential Equations, De Gruyter, Berlin, 1992.doi: 10.1515/9783110874228. |
[15] |
J. Duan, K. Lu and B. Schmalfuß, Invariant manifolds for stochastic partial differential equations, Ann. Probab., 31 (2003), 2109-2135.doi: 10.1214/aop/1068646380. |
[16] |
F. Flandoli and B. Schmalfuß, Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise, Stoch. Stoch. Rep., 59 (1996), 21-45.doi: 10.1080/17442509608834083. |
[17] |
G. Hines, Upper semicontinuity of the attractor with respect to parameter dependent delays, J. Differ. Equ., 123 (1995), 56-92.doi: 10.1006/jdeq.1995.1157. |
[18] |
A. V. Kapustian and J. Valero, Attractors of multivalued semiflows generated by differential inclusions and their approximations, Abstr. Appl. Anal., 5 (2000), 33-46.doi: 10.1155/S1085337500000191. |
[19] |
P. E. Kloeden and B. Schmalfuß, Asymptotic behaviour of nonautonomous difference inclusions, Systems Control Lett., 33 (1998), 275-280.doi: 10.1016/S0167-6911(97)00107-2. |
[20] |
P. E. Kloeden, Upper semicontinuity of attractors of delay differential equations in the delay, Bull. Austral. Math. Soc., 73 (2006), 299-306.doi: 10.1017/S0004972700038880. |
[21] |
P. E. Kloeden and J. A. Langa, Flattening, squeezing and the existence of random attractors, Proceedings of the Royal Society of London, 463 (2007), 163-181.doi: 10.1098/rspa.2006.1753. |
[22] |
D. S. Li, Y. J. Wang and S. Y. Wang, On the dynamics of nonautonomous general dynamical systems and differential inclusions, Set-Valued Anal., 16 (2008), 651-671.doi: 10.1007/s11228-007-0054-8. |
[23] |
Q. F. Ma, S. H. Wang and C. K. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana Univ. Math. J., 51 (2002), 1541-1559.doi: 10.1512/iumj.2002.51.2255. |
[24] |
V. S. Melnik and J. Valero, On attractors of multivalued semi-flows and differential inclusions, Set-Valued Anal., 6 (1998), 83-111.doi: 10.1023/A:1008608431399. |
[25] |
V. S. Melnik and J. Valero, On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions, Set-Valued Anal., 8 (2000), 375-403.doi: 10.1023/A:1026514727329. |
[26] |
B. Schmalfuß and K. R. Schneider, Invariant manifolds for random dynamical systems with slow and fast variables, J. Dynam. Differential Equations, 20 (2008), 133-164.doi: 10.1007/s10884-007-9089-7. |
[27] |
R. Temam, Infinite Dimensional Dynamical System in Mechanics and Physics, 2nd Edition, Springer-Verlag, New York, 1997.doi: 10.1007/978-1-4612-0645-3. |
[28] |
B. X. Wang, Upper semicontinuity of random attractors for non-compact random dynamical systems, Electron. J. Differ. Equ., 139 (2009), 1-18. |
[29] |
B. X. Wang, Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems, J. Differ. Equ., 253 (2012), 1544-1583.doi: 10.1016/j.jde.2012.05.015. |
[30] |
J. Y. Wang and Y. J. Wang, Pullback attractors for reaction-diffusion delay equations on unbounded domains with non-autonomous deterministic and stochastic forcing terms, J. Math. Phys., 54 (2013), 082703, 25 pp.doi: 10.1063/1.4817862. |
[31] |
X. H. Wang, K. N. Lu and B. X. Wang, Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing, SIAM J. Appl. Dyn. Syst., 14 (2015), 1018-1047.doi: 10.1137/140991819. |
[32] |
Y. H. Wang and Y. M. Qin, Upper semicontinuity of pullback attractors for nonclassical diffusion equation, J. Math. Phys., 51 (2010), 022701, 12 pp.doi: 10.1063/1.3277152. |
[33] |
Y. J. Wang and S. F. Zhou, Kernel sections and uniform attractors of multi-valued semiprocesses, J. Differ. Equ., 232 (2007), 573-622.doi: 10.1016/j.jde.2006.07.005. |
[34] |
Y. J. Wang, On the upper semicontinuity of pullback attractors for multi-valued processes, Quarterly of Applied Mathematics, 71 (2013), 369-399.doi: 10.1090/S0033-569X-2013-01306-1. |
[35] |
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. Differ. Equ., 259 (2015), 728-776.doi: 10.1016/j.jde.2015.02.026. |
[36] |
Y. C. You, Robustness of global attractors for reversible Gray-Scott systems, J. Dynam. Differential Equations, 24 (2012), 495-520.doi: 10.1007/s10884-012-9252-7. |
[37] |
Y. C. You, Random attractors and robustness for stochastic reversible reaction-diffusion systems, Discrete Contin. Dyn. Syst., 34 (2014), 301-333.doi: 10.3934/dcds.2014.34.301. |
[38] |
C. K. Zhong, M. H. Yang and C. Y. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations, J. Differ. Equ., 223 (2006), 367-399.doi: 10.1016/j.jde.2005.06.008. |
[39] |
W. Q. Zhao and Y. R. Li, $(L^2, L^p)$-random attractors for stochastic reaction-diffusion equation on unbounded domains, Nonlinear Anal. TMA, 75 (2012), 485-502.doi: 10.1016/j.na.2011.08.050. |
[40] |
S. F. Zhou, Upper-semicontinuity of attractors for random lattice systems perturbed by small white noises, Nonlinear Anal. TMA, 75 (2012), 2793-2805.doi: 10.1016/j.na.2011.11.022. |