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Abstrakty
We consider the convective Cahn-Hilliard equation with periodic boundary conditions. Based on the iteration technique for regularity estimates and the classical theorem on existence of a global attractor, we prove that the convective Cahn-Hilliard equation has a global attractor in Hk.
Słowa kluczowe
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Rocznik
Tom
Strony
53--64
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
autor
- School of Mathematics, Jilin University, Changchun, 130012, P.R. China, zhaoxp10@mails.jlu.edu.cn
Bibliografia
- [1] R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- [2] T. Dlotko, Global attractor for the Cahn-Hilliard equation in H2 and H3, J. Differential Equations 113 (1994), 381-393.
- [3] A. Eden and V. K. Kalantarov, 3D connective Cahn-Hilliard equation, Comm. Pure Appl. Anal. 6 (2007), 1075-1086.
- [4] A. Eden and V. K. Kalantarov, The convective Cahn-Hilliard equation, Appl. Math. Lett. 20 (2007), 455-461.
- [5] A. A. Golovin, S. H. Davis and A. A. Nepomnyashchy, A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth, Phys. D 122 (1998), 202-230.
- [6] A. A. Golovin, A. A. Nepomnyashchy, S. H. Davis and M. A. Zaks, Convective Cahn-Hilliard models: from coarsening to roughening, Phys. Rev. Lett. 86 (2001), 1550-1553.
- [7] K. H. Kwek, On the Cahn-Hilliard type equation, PhD thesis, Georgia Institute of Technology, 1991.
- [8] C. C. Liu, On the convective Cahn-Hilliard equation, Bull. Polish Acad. Sci. Math. 53 (2005), 299-314.
- [9] C. C. Liu, On the convective Cahn-Hilliard equation with degenerate mobility, J. Math. Anal. Appl. 344 (2008), 124-144.
- [10] T. Ma and S. H. Wang, Stability and Bifurcation of Nonlinear Evolution Equations, Sci. Press, Beijing, 2006 (in Chinese).
- [11] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, 1983.
- [12] L. Y. Song, Y. N. He and Y. D. Zhang, The existence of global attractors for semi-linear parabolic equation in Hk spaces, Nonlinear Anal. 68 (2008), 3541-3549.
- [13] L. Y. Song, Y. D. Zhang and T. Ma, Global attractor of the Cahn-Hilliard equation in Hk spaces, J. Math. Anal. Appl. 355 (2009), 53-62.
- [14] L. Y. Song, Y. D. Zhang and T. Ma, Global attractor of a modified Swift-Hohenberg equation in Hk spaces, Nonlinear Anal. 72 (2010), 183-191.
- [15] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, 1997.
- [16] M. A. Zarksm, A. Podolny, A. A. Nepomnyashchy and A. A. Golovin, Periodic stationary patterns governed by a convective Cahn-Hilliard equation, SIAM J. Appl. Math. 66 (2005), 700-720.
- [17] X. P. Zhao and C. C. Liu, Global attractor for the convective Cahn-Hilliard equation, Bull. Polish Acad. Sci. Math. 58 (2010), 117-127.
- [18] S. M. Zheng, Asymptotic behavior of solution to the Cahn-Hilliard equation, Appl. Anal. 23 (1986), 165-184.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0065-0036