REGULARITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC COUPLED REACTION-DIFFUSION SYSTEMS

Jinyan Yin; Yangrong Li; Anhui Gu

doi:10.11948/2017056

2017 Volume 7 Issue 3

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2017 > 7(3): 884-898

Next Article Previous Article

Jinyan Yin, Yangrong Li, Anhui Gu. REGULARITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC COUPLED REACTION-DIFFUSION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 884-898. doi: 10.11948/2017056

Citation:

Jinyan Yin, Yangrong Li, Anhui Gu. REGULARITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC COUPLED REACTION-DIFFUSION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 884-898. doi: 10.11948/2017056

REGULARITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC COUPLED REACTION-DIFFUSION SYSTEMS

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Fund Project:

Abstract

Abstract

We consider the dynamical behavior of the typical non-autonomous autocatalytic stochastic coupled reaction-diffusion systems on the entire space Rⁿ. Some new uniform asymptotic estimates are implemented to investigate the existence of pullback attractors in the Sobolev space H¹(Rⁿ)³ for the three-component reversible Gray-Scott system.
- Non-autonomous cocycle /
- bi-spatial pullback attractor /
- regularity of attractor /
- three-component reversible Gray-Scott system
MSC: 37L55;35R60;60H15;35B40;35K57

FullText(HTML)

References

[1]	L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1998. Google Scholar
[2]	P. Bates, H. Lisei and K. Lu, Attractors for stochastic lattice dynamical systems, Stoch. Dyn., 2006, 6(1), 1-21. Google Scholar
[3]	P. Bates, K. Lu and B. Wang, Random attractors for stochastic reactiondiffusion equations on unbounded domains, J. Differ. Equations, 2009, 246(2), 845-869. Google Scholar
[4]	H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Theory Relat. Fields, 1994, 100(3), 365-393. Google Scholar
[5]	A. Gu, Pullback D-attractors of non-autonomous three-component reversible Gray-Scott system on unbounded domains, Abstr. Appl. Anal., 2013, 2013(2), 1-13. Google Scholar
[6]	A. Gu, Random attractors of stochastic three-component reversible Gray-Scott system on unbounded domains, Abstr. Appl. Anal., 2012, 2012(7), 1-22. Google Scholar
[7]	A. Gu and H. Xiang, Upper semicontinuity of random attractors for stochastic three-component reversible Gray-Scott system, Appl. Math. Comput., 2013, 225(12), 387-400. Google Scholar
[8]	A. Gu, S. Zhou and Z. Wang, Uniform attractor of non-autonomous threecomponent reversible Gray-Scott system, Appl. Math. Comput., 2013, 219(16), 8718-8729. Google Scholar
[9]	P. Gray and S. Scott, Autocatalytic reactions in the isothermal continuous stirred tank reactor:Isolas and other forms of multistability, Chem. Eng. Sci., 1983, 38(1), 29-43. Google Scholar
[10]	P. Gray and S. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor:Oscillations and instabilities in the system a+2b → 3b,b → c, Chem. Eng. Sci., 1984, 39(6), 1087-1097. Google Scholar
[11]	P. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, American Mathematical Society, Providence, 2011. Google Scholar
[12]	Y. Li and B. Guo, Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction-diffusion equations, J. Differ. Equations, 2008, 245(7), 1775-1800. Google Scholar
[13]	Y. Li, A. Gu and J. Li, Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations, J. Differ. Equations, 2015, 258(2), 5040-534. Google Scholar
[14]	Y. Li and J. Yin, A modified proof of pullback attractors in a sobolev space for stochastic Fitzhugh-Nagumo equations, Disc. Cont. Dyn. Syst. Serie B., 2016, 21(4), 1203-1223. Google Scholar
[15]	G. Lukaszewicz, On pullback attractors in HH₀¹ for nonautonomous reactiondiffusion equations, Int. J. Bifurcat. Chaos, 2010, 20(9), 2637-2644. Google Scholar
[16]	H. Mahara, N. Suematsu, T. Yamaguchi, K. Ohgane, Y. Nishiura and M. Shimomura, Three-variable reversible Gray-Scott model, J. Chem. Physics, 2004, 121(18), 8968-8972. Google Scholar
[17]	I. Prigogine and R. Lefever, Symmetry-breaking instabilities in dissipative systems, J. Chem. Physics, 1968, 48(4), 1665-1700. Google Scholar
[18]	B. Schmalfuss, Backward cocycle and attractors of stochastic differential equations (in:V. Reitmann, T. Riedrich, N. Koksch, eds.), International Seminar on Applied Mathematics-Nonlinear Dynamics:Attractor Approximation and Global Behavior, Technische Universität, Dresden, 1992, 185-192. Google Scholar
[19]	S. Scott and K. Showalter, Simple and complex reaction-diffusion fronts, Chemical Waves and Patterns (R. Kapral and K. Showalter, eds.), Understanding Chemical Reactivity, Springer, 1995, 10, 485-516. Google Scholar
[20]	B. Wang, Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems, J. Differ. Equations, 2012, 253(5), 1544-1583. Google Scholar
[21]	B. Wang, Pullback attractors for non-autonomous reaction-diffusion equations on Rn, Front. Math. China, 2009, 4(3), 563-583. Google Scholar
[22]	F. Yin and L. Liu, D-pullback attractor for a non-autonomous wave equation with additive noise on unbounded domains, Comput. Math. Appl., 2014, 68(3), 424-438. Google Scholar
[23]	Y. You, Dynamics of three-component reversible Gray-Stott model, Disc. Cont. Dyn. Syst. Serie B., 2010, 14(4), 1671-1688. Google Scholar
[24]	Y. You, Robustness of global attractors for reversible Gray-Scott systems, J. Dyn. Differ. Equat., 2012, 24(3), 495-520. Google Scholar
[25]	Y. You, Random attractors and robustness for stochastic reversible reactiondiffusion systems, Disc. Cont. Dyn. Syst. Serie A., 2014, 34(1), 301-333. Google Scholar
[26]	Y. You, Random dynamics of stochastic reaction-diffusion systems with additive noise, J. Dyn. Differ. Equat., 2015, 29(1), 82-112. DOI:10.1007/s10884-015-9431-4. Google Scholar
[27]	Y. You, Dynamics of two-compartment Gray-Scott equations, Nonlinear Anal., 2011, 74(5), 1969-1986. Google Scholar
[28]	W. Zhao, Regularity of random attractors for a degenerate parabolic equations driven by additive noise, Appl. Math. Comput., 2014, 239(15), 358-374. Google Scholar
[29]	C. Zhong, M. Yang and C. Sun, The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reactiondiffusion equations, J. Differ. Equations, 2006, 223(2), 367-399. Google Scholar