Cahn-Hilliard-Brinkman系统的全局吸引子

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O175.2

Xiangyu Xiao,Zhilin Pu. The Global Attractors of Cahn-Hilliard-Brinkman System[J].Acta mathematica scientia,Series A, 2022, 42(4): 1027-1040.

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1	Brinkman H C . A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Applied Scientific Research, 1949, 1 (1): 727- 734
2	Eden A , Kalantarov V K . The convective Cahn-Hilliard equation. Applied Mathematics Letters, 2007, 20 (4): 455- 461 doi: 10.1016/j.aml.2006.05.014
3	Abels H . On a diffusive interface model for two-phase flows of viscous, incompressible fluids with matched densities. Arch Ration Mech Anal, 2009, 194 (2): 463- 506 doi: 10.1007/s00205-008-0160-2
4	Zhou Y , Fan J . The vanishing viscosity limit for a 2D Cahn-Hilliard-Navier-Stokes system with a slip boundary condition. Nonlinear Anal Real World Appl, 2013, 14 (2): 1130- 1134 doi: 10.1016/j.nonrwa.2012.09.003
5	Starovoitov V N . The dynamics of a two-component fluid in the presence of capillary forces. Math Notes, 1997, 62 (2): 244- 254 doi: 10.1007/BF02355911
6	X Wang , H Wu . Long-time behavior for the Hele-Shaw-Cahn-Hilliard system. J Asymptot Anal, 2012, 78 (4): 217- 245
7	Jiang J , Wu H , Zheng S M . Well-posedness and long-time behavior of solutions for a non-autonomous Cahn-Hilliard-Darcy system with mass source modeling tumor growth. Differential Equations, 2015, 259 (7): 3032- 3077 doi: 10.1016/j.jde.2015.04.009
8	Feng X B , Wise S . Analysis of a Darcy-Cahn-Hilliard diffuse interface model for the Hele-Shaw flow and its fully discrete finite element approximation. SIAM J Numer Anal, 2012, 50 (3): 1320- 1343 doi: 10.1137/110827119
9	Luis C , Maria G , Nicola Z . Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Communications in Partial Differential Equations, 2020, 45 (12): 1799- 1819 doi: 10.1080/03605302.2020.1814325
10	Cahn J W , Hilliard J E . Free energy of a nonuniform system I: Interfacial free energy. Chem Phys, 1958, 28 (2): 258- 267
11	Elliott C M , Zheng S . On the Cahn-Hilliard equation. Arch Rational Mech Anal, 1986, 96 (8): 339- 357
12	Liu C , Shen J . A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier spectral method. Phys D, 2003, 179 (3): 211- 228
13	Schmuck M , Pradas M , Pavliotis G A , Kalliadasis S . Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media. Nonlinearity, 2013, 26 (12): 3259- 3277 doi: 10.1088/0951-7715/26/12/3259
14	Zhong C K , Yang M H , Sun C Y . The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations. Differential Equations, 2006, 223 (2): 367- 399 doi: 10.1016/j.jde.2005.06.008
15	Grinfeld M , Novick-Cohen A . The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor. Tran, 1999, 351 (6): 351- 356
16	Nicolaenko B , Scheurer B , Temam R . Some global dynamical properties of a class of pattern formation equations. Comm Partial Differential Equations, 1989, 14 (2): 245- 297 doi: 10.1080/03605308908820597
17	Bosia S , Conti M , Grasselli M . On the Cahn-Hilliard-Brinkman system. Commun Math Sci, 2015, 13 (6): 1541- 1567 doi: 10.4310/CMS.2015.v13.n6.a9
18	Li F , Zhong C K , You B . Finite-dimensional global attractor of the Cahn-Hilliard-Brinkman system. Journal of Mathematical Analysis and Applications, 2016, 434 (1): 599- 616 doi: 10.1016/j.jmaa.2015.09.026
19	You B . Global attractor of the Cahn-Hilliard-Navier-Stokes system with moving contact lines. American Institute of Mathematical Sciences, 2019, 18 (5): 2283- 2298
20	Zhao X P , Liu C C . On the existence of global attractor for 3D viscous Cahn-Hilliard equation. Acta Appl Math, 2015, 138 (1): 199- 212 doi: 10.1007/s10440-014-9963-3

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The Global Attractors of Cahn-Hilliard-Brinkman System

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