[1] Zelik S V. The attractor for a nonlinear reaction-diffusion system with a supercritical nonlinearity and its dimension. Rend Accad Naz Sci XL Mem Mat Appl, 2000, 24:1-25
[2] Temam R. Infinite-dimensional Dynamical Systems in Mechanics and Physics. New York:Springer, 1997
[3] Dung L, Nicolaenko B. Exponential attractors in Banach spaces. J Dynam Differ Equ, 2001, 13:791-806
[4] Zhong Y S, Zhong C K. Exponential attractors for semigroups in Banach spaces. Nonlinear Anal, 2012, 75(4):1799-1809
[5] Efendiev M, Miranville A. The dimension of the global attractors for dissipative reaction-diffusion systems. Appl Math Lett, 2003, 16(3):351-355
[6] Debussche A, Temam R. Inertial manifolds and their dimension//Anderson S I, Anderson A E, Ottason O. Dynamical systems, Theory and Applications. Singapore:World Scientific, 1993
[7] Eden A, et al. Inertial sets for dissipative evolution equations. Minneapolis:University of Minnesota, 1990
[8] Foias C, Manley O, Temam R. Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. Math Modell Numer Anal, 1988, 22:93-118
[9] Mallet-Paret J, Sell G. Inertial manifolds for reaction-diffusion equations in higher space dimensions. J Amer Math Soc, 1988, 1(4):805-866
[10] Robinson J C. Infinite-dimensional Dynamical Systems an Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. Cambridge University Press, 2001
[11] Sell G R, You Y C. Dynamics of Evolutionary Equations. New York:Springer, 2002
[12] Babin A, Vishik M I. Attractors of Evolution Equations. Amsterdam:North-Holland, 1992
[13] Efendiev M, Zelik S V. The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Comm Pure Appl Math, 2001, 54:0625-0688
[14] Zhong C K, Yang M H, Sun C Y. The existence of global attractors for norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations. J Differ Equ, 2006, 223(2):367-399
[15] Sun C Y. Asymptotic regularity for some dissipative equations. J Differ Equ, 2010, 248(2):342-362
[16] Zhong C K, You B, Yang R. The existence of multiple equilibrium points in a global attractor for some symmetric dynamical systems. Nonlinear Analysis:RWA, 2014, 19:31-44
[17] Gilbarg D, Trudinger N S. Elliptic partial differential equation of second order. Berlin:Springer-Verlag, 2001
[18] Evans L C. Partial Differential Equations. Grad Stud Math. Vol 19. Providence, RI:AMS, 1998
[19] Ouhabaz E M. Analysis of Heat Equations on Domains. Princeton University Press, 2005
[20] Robinson J C. Dimensions, Imbeddings and Attractors. Cambridge University Press, 2011 |