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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 8
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Original Articles

Global attractors for the 3D viscous Cahn–Hillard equations in an unbounded domain

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Pages 1157-1171 | Received 15 Jun 2009, Accepted 30 Jun 2009, Published online: 21 Sep 2010

References

  • Eden , A and Kalantarov , VK . 2007 . The convective Cahn–Hillard equation . Appl. Math. Lett. , 20 : 455 – 461 .
  • Eden , A and Kalantarov , VK . 2007 . 3D convective Cahn–Hillard equation . Commun. Pure and Appl. Anal. , 6 : 1075 – 1086 .
  • Sun , Chun-you and Zhong , Cheng-kui . 2005 . Attractors for the semilinear reaction-diffusion equation with distribution derivatives in unbounded domains . Nonlinear Anal. , 63 : 49 – 65 .
  • Bonfoh , Ahmed . 2006 . Finite-dimensional attractor for the viscous Cahn–Hillard equation in an unbounded domain . Quart. Appl. Math. , LXIV ( 1 ) : 93 – 104 .
  • Bonfoh , A and Miranville , A . 2001 . On Cahn–Hillard–Gurtin equations (Proceedings of the 3rd World Congress of Nonlinear Analysists) . Nonlinear Anal. , 47 : 3455 – 3466 .
  • Cahn , JW . 1961 . On spinodal decomposition . Acta Metall. , 9 : 795 – 801 .
  • Cahn , JW and Hillard , JE . 1958 . Free energy of a non-uniform system I. Interfacial free energy . J. Chem. Phys. , 2 : 258 – 267 .
  • Efendiev , M and Miranvile , A . 1999 . Finite dimensional attractors for a reaction diffusion equation in ℝ n with a strong nonlinearity . Discrete Contin. Dyn. Syst. , 5 ( 2 ) : 399 – 424 .
  • Ghidaglia , JM . 1994 . A note on the strong convergence towards attractors for damped KdV equations . J. Differential Equations , 110 : 356 – 359 .
  • Ladyzhenskaya , OA . 1987 . On the determination of minimal global attractors for the Navier–Stokes and other partial differential equations . Russian Math. Surveys , 42 ( 6 ) : 27 – 73 .
  • Miranville , A , Pietrus , A and Rakotosun , JM . 1988 . Dynamical aspect of a generalized Cahn–Hillard equation on a microbalance force . Asymptotic Anal. , 16 : 315 – 345 .
  • Ball , JM . 1997 . Continuity properties and global attractors of generalized semiflows and the Navier–Stokes equations . J. Nonlinear Sci. , 7 : 475 – 502 .
  • Ball , JM . 2004 . Global Attractors for damped semilinear wave equations . Discrete Contin. Dyn. Syst. , 10 : 31 – 52 .
  • Antoci , F and Prizzi , M . 2001 . Reaction diffusion equations on unbounded domains . Topol. Methods Nonlinear Anal. , 18 : 229 – 259 .
  • Antoci , F and Prizzi , M . 2002 . Attractors and global averaging of non-autonomous reaction-diffusion equations in ℝ n . Topol. Methods Nonlinear Anal. , 20 : 229 – 259 .
  • Arrieta , JM , Cholewa , JW , Dlotko , T and Rodriguez-Bernal , A . 2000 . Asymptotic behaviour and attractors for reaction diffusion equations in unbounded domains . Nonlinear Anal. , 56 : 515 – 554 .
  • Astaburuaga , AM , Bisognin , E , Bisognin , V and Fernandez , C . 1998 . Global attractors and finite dimensionality for a class of dissipative equations of BBM's type . Electronic J. Diff. Equ. , 25 : 1 – 14 .
  • Efendiev , M , Miranvile , A and Zelik , S . 2004 . Exponential Attractors for a singularly perturbed Cahn–Hillard system . Math. Nachrichten , 271 ( 1 ) : 11 – 31 .
  • Hale , JK . 1988 . Asymptotic Behavior of Dissipative Systems , Providence, RI : American Mathematical Society .
  • Miranville , A . 2000 . Some generalization of the Cahn–Hillard equation . Asymptotic Anal. , 22 : 235 – 259 .
  • Morillas , F and Valero , J . 2005 . Attractors for reaction-diffusion equations in ℝ n with continuous nonlinearity . Asymptotic Anal. , 44 : 111 – 130 .
  • Moise , I and Rossa , R . 1997 . On the regularity of the global attractor of a weakly damped KdV equation . Adv. Differ. Equ. , 2 : 257 – 296 .
  • Moise , I , Rossa , R and Wang , X . 1998 . Attractors for noncompact semigroups via energy equations . Nonlinearity , 11 : 1369 – 1393 .
  • Polat , M . 2009 . Attractor for a generalized 2D parabolic system on an unbounded domain . Appl. Anal. , 88 ( 1 ) : 63 – 74 .
  • Prizzi , M . 2005 . Averaging, Conley index continuation and recurrent dynamics in almost-periodic equation . J. Differential Equations , 210 : 429 – 451 .
  • Rodrigue-Bernal , A and Wang , B . 2000 . Attractors for partly dissipative reaction diffusion systems in ℝ n . J. Math. Anal. Appl. , 252 : 790 – 803 .
  • Sell , G and You , Y . 2002 . Dynamics of Evolutionary Equations , New York : Springer .
  • Temam , R . 1988 . Infinite-dimensional Dynamical Systems in Mechanics and Physics , New York : Springer .
  • Wang , B , Fussner , DW and Bi , C . 2007 . Existence of global attractors for the Benjamin–Bona–Mahony equation in unbounded domains . J. Phys. A: Math. Theor. , 40 : 10491 – 10504 .
  • Babin , AV and Vishik , MI . 1992 . Attractors of Evolution Equations , Amsterdam : North-Holland Publishing Co. .

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