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The existence of global attractor for convective Cahn-Hilliard equation

Bo Liu|Xiaopeng Zhao
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회지 (Journal of the KMS)|제49권 제2호|pp. 357-378

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attractorconvective Cahn-Hilliard equationabsorbing set
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초록

In this paper, we consider the convective Cahn-Hilliard equa-tion. Based on the regularity estimates for the semigroups, iteration tech-nique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in Hk (k≥ 0) space, which attracts any bounded subset of Hk(Ω) in the Hk-norm.

Abstract

In this paper, we consider the convective Cahn-Hilliard equa-tion. Based on the regularity estimates for the semigroups, iteration tech-nique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in Hk (k≥ 0) space, which attracts any bounded subset of Hk(Ω) in the Hk-norm.

참고문헌 (20)

  1. J. W. Cholewa, "Global attractor for the Cahn-Hilliard system", Bull. Austral. Math. Soc, 49(2), pp.277~292 (1994)
  2. T. Dlotko, "Global attractor for the Cahn-Hilliard equation in H2 and H3", J. Differential Equations, 113(2), pp.381~393 (1994)
  3. A. Eden, "The convective Cahn-Hilliard equation", Appl. Math. Lett, 20(4), pp.455~461 (2007)
  4. A. Eden, "3D convective Cahn-Hilliard equation", Commun. Pure Appl. Anal, 6(4), pp.1075~1086 (2007)
  5. A. A. Golovin, "A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth", Phys. D, 122(1), pp.202~230 (1998)
  6. K. H. Kwek, "On the Cahn-Hilliard type equation", 박사, pp.1991
  7. D. Li, "Global attractor for the Cahn-Hilliard system with fast growing nonlinearity", J. Differential Equations, 149(2), pp.191~210 (1998)
  8. C. Liu, "On the convective Cahn-Hilliard equation", Bull. Pol. Acad. Sci. Math, 53(3), pp.299~314 (2005)
  9. C. Liu, "On the convective Cahn-Hillirad equation with degenerate mobility", J. Math. Anal. Appl, 344(1), pp.124~144 (2008)
  10. T. Ma, "Stability and Bifurcation of Nonlinear Evolution Equations" (2006), Science Press
  11. A. Pazy, "Semigroups of linear operators and applications to partial differential equations", Appl. Math. Sci, 44 (1983), Springer-Verlag
  12. A. Podolny, "Dynamics of domain walls governed by the convective Cahn-Hilliard equation", Phys. D, 201(3), pp.291~305 (2005)
  13. L. Song, "The existence of global attractors for semilinear parabolic equation in Hk space", Nonlinear Anal, 68(11), pp.3541~3549 (2008)
  14. L. Song, "Global attractor of the Cahn-Hilliard equation in Hk spaces", J. Math. Anal. Appl, 355(1), pp.53~62 (2009)
  15. L. Song, "Global attractor of a modi ed Swift-Hohenberg equation in Hk space", Nonlinear Anal, 72(1), pp.183~191 (2010)
  16. R. Temam, "In nite-Dimensional Dynamical Systems in Mechanics and Physics" (1988), Springer
  17. S. J. Watson, "Coarsening dynamics of the convective Cahn-Hilliard equations", Phys. D, 178, pp.127~148 (2003)
  18. H. Wu, "Global attractor for the 1-D thin film equation", Asymptot. Anal, 51(2), pp.101~111 (2007)
  19. M. A. Zarks, "Periodic stationary patterns governed by a convective Cahn-Hilliard equation", SIAM J. Appl. Math, 66(2), pp.700~720 (2005)
  20. X. Zhao, "Global attractor for the convective Cahn-Hilliard equation", Bull. Pol. Acad. Sci. Math, 58(2), pp.117~127 (2010)

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