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Random attractor of stochastic Brusselator system with multiplicative noise
1. | Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States |
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P. W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction-diffusion equations on unbounded domains, J. Differential Equations, 246 (2009), 845-869.
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T. Caraballo, J. A. Langa and J. C. Robinson, A stochastic pitchfork bifurcation in a reaction-diffusion equation, Proc. R. Soc. Lond. A, 457 (2001), 2041-2061.
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V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, AMS Colloquium Publications, Vol. 49, AMS, Providence, RI, 2002. |
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M. Ghergu and V. D. Rădulescu, Nonlinear PDEs: Mathematical Modles in Biology, Chemistry and Population Genetics, Springer, Berlin Heidelberg, 2012.
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P. E. Kloeden and J. A. Langa, Flattening, squeezing and the existence of random attractors, Proc. Royal Soc. London, Ser. A, 463 (2007), 163-181.
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L. Prigogine and R. Lefever, Symmetry-breaking instabilities in dissipative systems, J. Chem. Physics, 48 (1968), 1695-1700. |
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J. C. Robinson, Stability of random attractors under perturbation and approximation, Journal of Differential Equations, 186 (2002), 652-669.
doi: 10.1016/S0022-0396(02)00038-4. |
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J. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge Univ. Press, Cambridge, UK, 2001.
doi: 10.1007/978-94-010-0732-0. |
[14] |
R. Sell and Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4757-5037-9. |
[15] |
B. Wang, Random attractors for non-autonomous stochastic wave equations with multiplicative noise, Discrete and Continuous Dynamical Systems-Series A, 34 (2014), 269-300.
doi: 10.3934/dcds.2014.34.269. |
[16] |
Y. You, Global dynamics and robustness of reversible autocatalytic reaction-diffusion systems, Nonl. Anal. A, 75 (2012), 3049-3071.
doi: 10.1016/j.na.2011.12.002. |
[17] |
Y. You, Random attractors and robustness for stochastic reversible reaction-diffusion systems, Discrete and Continuous Dynamical Systems - Series A, 34 (2014), 301-333.
doi: 10.3934/dcds.2014.34.301. |
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W. Zhao, $H^1$-random attractors for stochastic reaction-diffusion equations with additive noise, Nonl. Anal. A, 84 (2013), 61-72.
doi: 10.1016/j.na.2013.01.014. |
show all references
References:
[1] |
L. Arnold, Random Dynamical Systems, Springer-Verlag, 1998.
doi: 10.1007/978-3-662-12878-7. |
[2] |
A. V. Babin and M. I. Vishik, Regular attractors of semigroups of evolutionary equations, J. Math. Pures Appl., 62 (1983), 441-491. |
[3] |
P. W. Bates, K. Lu and B. Wang, Random attractors for stochastic reaction-diffusion equations on unbounded domains, J. Differential Equations, 246 (2009), 845-869.
doi: 10.1016/j.jde.2008.05.017. |
[4] |
T. Caraballo, J. A. Langa and J. C. Robinson, A stochastic pitchfork bifurcation in a reaction-diffusion equation, Proc. R. Soc. Lond. A, 457 (2001), 2041-2061.
doi: 10.1098/rspa.2001.0819. |
[5] |
V. V. Chepyzhov and M. I. Vishik, Attractors for Equations of Mathematical Physics, AMS Colloquium Publications, Vol. 49, AMS, Providence, RI, 2002. |
[6] |
H. Crauel, A. Debussche and F. Flandoli, Random attractors, J. Dyn. Diff. Eqns., 9 (1997), 307-341.
doi: 10.1007/BF02219225. |
[7] |
H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Th. Re. Fields, 100 (1994), 365-393.
doi: 10.1007/BF01193705. |
[8] |
F. Flandoli and B. Schmalfu$\beta$, Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative noise, Stoch. Stoch. Rep., 59 (1996), 21-45.
doi: 10.1080/17442509608834083. |
[9] |
M. Ghergu and V. D. Rădulescu, Nonlinear PDEs: Mathematical Modles in Biology, Chemistry and Population Genetics, Springer, Berlin Heidelberg, 2012.
doi: 10.1007/978-3-642-22664-9. |
[10] |
P. E. Kloeden and J. A. Langa, Flattening, squeezing and the existence of random attractors, Proc. Royal Soc. London, Ser. A, 463 (2007), 163-181.
doi: 10.1098/rspa.2006.1753. |
[11] |
L. Prigogine and R. Lefever, Symmetry-breaking instabilities in dissipative systems, J. Chem. Physics, 48 (1968), 1695-1700. |
[12] |
J. C. Robinson, Stability of random attractors under perturbation and approximation, Journal of Differential Equations, 186 (2002), 652-669.
doi: 10.1016/S0022-0396(02)00038-4. |
[13] |
J. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge Univ. Press, Cambridge, UK, 2001.
doi: 10.1007/978-94-010-0732-0. |
[14] |
R. Sell and Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4757-5037-9. |
[15] |
B. Wang, Random attractors for non-autonomous stochastic wave equations with multiplicative noise, Discrete and Continuous Dynamical Systems-Series A, 34 (2014), 269-300.
doi: 10.3934/dcds.2014.34.269. |
[16] |
Y. You, Global dynamics and robustness of reversible autocatalytic reaction-diffusion systems, Nonl. Anal. A, 75 (2012), 3049-3071.
doi: 10.1016/j.na.2011.12.002. |
[17] |
Y. You, Random attractors and robustness for stochastic reversible reaction-diffusion systems, Discrete and Continuous Dynamical Systems - Series A, 34 (2014), 301-333.
doi: 10.3934/dcds.2014.34.301. |
[18] |
W. Zhao, $H^1$-random attractors for stochastic reaction-diffusion equations with additive noise, Nonl. Anal. A, 84 (2013), 61-72.
doi: 10.1016/j.na.2013.01.014. |
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