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November  2016, 15(6): 2221-2245. doi: 10.3934/cpaa.2016035

Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice systems with random coupled coefficients

1. 

School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

2. 

Department of Mathematics, Zhejiang Normal University, Jinhua, 321004

Received  January 2016 Revised  June 2016 Published  September 2016

In this paper, we consider the existence of random attractors in a weighted space $ l_\rho ^2 $ for first-order non-autonomous stochastic lattice system with random coupled coefficients and multiplicative/additive white noise, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.
Citation: Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice systems with random coupled coefficients. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2221-2245. doi: 10.3934/cpaa.2016035
References:
[1]

2nd edition, Elsevier Ltd., 2003.  Google Scholar

[2]

Springer-Verlag, New York and Berlin, 1998.  Google Scholar

[3]

Internat. J. Bifur. Chaos., 11 (2001), 143-153. doi: 10.1142/s0218127401002031.  Google Scholar

[4]

Stoch. Dyn., 6 (2006), 1-21. doi: 10.1142/S0219493706001621.  Google Scholar

[5]

J. Differential Equations, 246 (2009), 845-869.  Google Scholar

[6]

Physica D, 289 (2014), 32-50. doi: 10.1016/j.physd.2014.08.004.  Google Scholar

[7]

Springer-Verlag, New York, 2002.  Google Scholar

[8]

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 10 (2003), 491-513.  Google Scholar

[9]

Front. Math. China, 3 (2008), 317-335. doi: 10.1007/s11464-008-0028-7.  Google Scholar

[10]

Nonlinear Anal., 130 (2016), 255-278. doi: 10.1016/j.na.2015.09.025.  Google Scholar

[11]

J. Dyn. Diff. Eqns., 9 (1997), 307-341.  Google Scholar

[12]

Probab. Th. Re. Fields, 100 (1994), 365-393. doi: 10.1007/bf01193705.  Google Scholar

[13]

Ann. Probab., 31 (2003), 2109-2135.  Google Scholar

[14]

Stochastics: An Inter. J. Probability and Stoch. Processes., 59 (1996), 21-45.  Google Scholar

[15]

J. Differential Equations, 73 (1988), 197-214. doi: 10.1016/0022-0396(88)90104-0.  Google Scholar

[16]

J. Differential Equations, 250 (2011), 1235-1266. doi: 10.1016/j.jde.2010.10.018.  Google Scholar

[17]

J. Math. Anal. Appl., 376 (2011), 481-493. doi: 10.1016/j.jmaa.2010.11.032.  Google Scholar

[18]

Phys. D., 233 (2007), 83-94. doi: 10.1016/j.physd.2007.06.008.  Google Scholar

[19]

Chaos Solitons Fractals, 27 (2006), 1080-1090. doi: 10.1016/j.chaos.2005.04.089.  Google Scholar

[20]

Phys. D., 221 (2006), 157-169. doi: 10.1016/j.physd.2006.07.023.  Google Scholar

[21]

Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.  Google Scholar

[22]

Commu. Math. Phys., 93 (1984), 285-300. doi: 10.1142/9789812833709_0019.  Google Scholar

[23]

Journal of American Mathematical Society, 6 (1993), 503-568. doi: 10.1090/s0894-0347-1993-1179539-4.  Google Scholar

[24]

Phys. D., 212 (2005), 317-336. doi: 10.1016/j.physd.2005.10.006.  Google Scholar

[25]

J. Differential Equations, 221 (2006), 224-245. doi: 10.1016/j.jde.2005.01.003.  Google Scholar

[26]

J. Math. Anal. Appl., 331 (2007), 121-136. doi: 10.1016/j.jmaa.2006.08.070.  Google Scholar

[27]

J. Differential Equations, 253 (2012), 1544-1583. doi: 10.1016/j.jde.2012.05.015.  Google Scholar

[28]

Stochastics and Dynamics, 14 (2014), 31 pages. doi: 10.1142/s0219493714500099.  Google Scholar

[29]

J. Difference Eqns. Appl., 14 (2008), 799-817. doi: 10.1080/10236190701859542.  Google Scholar

[30]

Nonlinear Anal., 72 (2010), 483-494. doi: 10.1016/j.na.2009.06.094.  Google Scholar

[31]

Discrete Contin. Dyn. Syst., 21 (2008), 643-663. doi: 10.3934/dcds.2008.21.643.  Google Scholar

[32]

Nonlinear Anal., 70 (2009), 1330-1348. doi: 10.1016/j.na.2008.02.015.  Google Scholar

[33]

Nonlinearity, 20 (2007), 1987-2006. doi: 10.1088/0951-7715/20/8/010.  Google Scholar

[34]

J. Math. Anal. Appl., 354 (2009), 78-95. doi: 10.1016/j.jmaa.2008.12.036.  Google Scholar

[35]

J. Differential Equations, 179 (2002), 605-624. doi: 10.1006/jdeq.2001.4032.  Google Scholar

[36]

Phys. D., 178 (2003), 51-61. doi: 10.1016/s0167-2789(02)00807-2.  Google Scholar

[37]

J. Differential Equations, 224 (2006), 172-204. doi: 10.1016/j.jde.2005.06.024.  Google Scholar

[38]

J. Differential Equations, 200 (2004), 342-368. doi: 10.1016/j.jde.2004.02.005.  Google Scholar

[39]

J. Math. Anal. Appl., 395 (2012), 42-55. doi: 10.1016/j.jmaa.2012.04.080.  Google Scholar

[40]

Discrete Contin. Dyn. Syst. Ser. B., 9 (2008), 763-785.  Google Scholar

show all references

References:
[1]

2nd edition, Elsevier Ltd., 2003.  Google Scholar

[2]

Springer-Verlag, New York and Berlin, 1998.  Google Scholar

[3]

Internat. J. Bifur. Chaos., 11 (2001), 143-153. doi: 10.1142/s0218127401002031.  Google Scholar

[4]

Stoch. Dyn., 6 (2006), 1-21. doi: 10.1142/S0219493706001621.  Google Scholar

[5]

J. Differential Equations, 246 (2009), 845-869.  Google Scholar

[6]

Physica D, 289 (2014), 32-50. doi: 10.1016/j.physd.2014.08.004.  Google Scholar

[7]

Springer-Verlag, New York, 2002.  Google Scholar

[8]

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 10 (2003), 491-513.  Google Scholar

[9]

Front. Math. China, 3 (2008), 317-335. doi: 10.1007/s11464-008-0028-7.  Google Scholar

[10]

Nonlinear Anal., 130 (2016), 255-278. doi: 10.1016/j.na.2015.09.025.  Google Scholar

[11]

J. Dyn. Diff. Eqns., 9 (1997), 307-341.  Google Scholar

[12]

Probab. Th. Re. Fields, 100 (1994), 365-393. doi: 10.1007/bf01193705.  Google Scholar

[13]

Ann. Probab., 31 (2003), 2109-2135.  Google Scholar

[14]

Stochastics: An Inter. J. Probability and Stoch. Processes., 59 (1996), 21-45.  Google Scholar

[15]

J. Differential Equations, 73 (1988), 197-214. doi: 10.1016/0022-0396(88)90104-0.  Google Scholar

[16]

J. Differential Equations, 250 (2011), 1235-1266. doi: 10.1016/j.jde.2010.10.018.  Google Scholar

[17]

J. Math. Anal. Appl., 376 (2011), 481-493. doi: 10.1016/j.jmaa.2010.11.032.  Google Scholar

[18]

Phys. D., 233 (2007), 83-94. doi: 10.1016/j.physd.2007.06.008.  Google Scholar

[19]

Chaos Solitons Fractals, 27 (2006), 1080-1090. doi: 10.1016/j.chaos.2005.04.089.  Google Scholar

[20]

Phys. D., 221 (2006), 157-169. doi: 10.1016/j.physd.2006.07.023.  Google Scholar

[21]

Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.  Google Scholar

[22]

Commu. Math. Phys., 93 (1984), 285-300. doi: 10.1142/9789812833709_0019.  Google Scholar

[23]

Journal of American Mathematical Society, 6 (1993), 503-568. doi: 10.1090/s0894-0347-1993-1179539-4.  Google Scholar

[24]

Phys. D., 212 (2005), 317-336. doi: 10.1016/j.physd.2005.10.006.  Google Scholar

[25]

J. Differential Equations, 221 (2006), 224-245. doi: 10.1016/j.jde.2005.01.003.  Google Scholar

[26]

J. Math. Anal. Appl., 331 (2007), 121-136. doi: 10.1016/j.jmaa.2006.08.070.  Google Scholar

[27]

J. Differential Equations, 253 (2012), 1544-1583. doi: 10.1016/j.jde.2012.05.015.  Google Scholar

[28]

Stochastics and Dynamics, 14 (2014), 31 pages. doi: 10.1142/s0219493714500099.  Google Scholar

[29]

J. Difference Eqns. Appl., 14 (2008), 799-817. doi: 10.1080/10236190701859542.  Google Scholar

[30]

Nonlinear Anal., 72 (2010), 483-494. doi: 10.1016/j.na.2009.06.094.  Google Scholar

[31]

Discrete Contin. Dyn. Syst., 21 (2008), 643-663. doi: 10.3934/dcds.2008.21.643.  Google Scholar

[32]

Nonlinear Anal., 70 (2009), 1330-1348. doi: 10.1016/j.na.2008.02.015.  Google Scholar

[33]

Nonlinearity, 20 (2007), 1987-2006. doi: 10.1088/0951-7715/20/8/010.  Google Scholar

[34]

J. Math. Anal. Appl., 354 (2009), 78-95. doi: 10.1016/j.jmaa.2008.12.036.  Google Scholar

[35]

J. Differential Equations, 179 (2002), 605-624. doi: 10.1006/jdeq.2001.4032.  Google Scholar

[36]

Phys. D., 178 (2003), 51-61. doi: 10.1016/s0167-2789(02)00807-2.  Google Scholar

[37]

J. Differential Equations, 224 (2006), 172-204. doi: 10.1016/j.jde.2005.06.024.  Google Scholar

[38]

J. Differential Equations, 200 (2004), 342-368. doi: 10.1016/j.jde.2004.02.005.  Google Scholar

[39]

J. Math. Anal. Appl., 395 (2012), 42-55. doi: 10.1016/j.jmaa.2012.04.080.  Google Scholar

[40]

Discrete Contin. Dyn. Syst. Ser. B., 9 (2008), 763-785.  Google Scholar

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