Global attractor for the convective Cahn-Hilliard equation

• Autorzy: Zhao X. , Liu C.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H2.

Słowa kluczowe

EN

global attractor; convective Cahn-Hilliard equation; w-limit set

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 2
• Strony: 117--127
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Zhao X.

autor

Liu C.

• Department of Mathematics Jilin University, Changchun 130012, P.R. China,

Bibliografia

• [1] J. W. Cholewa and T. Dlotko, Global attractor for the Cahn-Hilliard system, Bull. Austral. Math. Soc. 49 (1994), 277-292.
• [2] T. Dlotko, Global attractor for the Cahn-Hilliard equation in H2 and H3, J. Diffreential Equations 113 (1994), 381-393.
• [3] A. Eden and V. K. Kalantarov, The convective Cahn-Hilliard equation, Appl. Math. Lett. 20 (2007), 455-461.
• [4] A. Eden and V. K. Kalantarov, 3D convective Cahn-Hilliard equation, Comm. Pure Appl. Anal. 6 (2007) 1075-1086.
• [5] A. A. Golovin, S. H. Davis and A. A. Nepomnyashchy, A convective Cahn-Hillard model for the formation of facets and corners in crystal growth, Phys. D 122 (1998), 202-230.
• [6] K. H. Kwek, On the Cahn-Hilliard type equation, PhD thesis, Georgia Institute of Technology, 1991.
• [7] D. S. Li and C. K. Zhong, Global attractor for the Cahn-Hilliard system with fast growing nonlinearity, J. Differential Equations 149 (1998), 191-210.
• [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] R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.
• [11] S. J. Watson, F. Otto, B. Y. Rubinstein and S. H. Davis, Coarsening dynamics of the convective Cahn-Hilliard equations, Phys. D 178 (2003), 127-148.
• [12] H. Wu and S. M. Zheng, Global attractor for the 1-D thin film equation, Asymptotic Anal. 51 (2007), 101-111.
• [13] M. A. Zaks, 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.