On the connective Cahn-Hilliard equation

• Autorzy: Liu C.

Identyfikatory

DOI

10.4064/ba53-3-8

• Języki publikacji: EN

Abstrakty

EN

The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.

Słowa kluczowe

EN

convective Cahn-Hilliard equation; existence; instability

PL

istnienie; niestabilność

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 3
• Strony: 299--314
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Liu C.

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

Bibliografia

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• [3] С. M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27 (1996), 404-423.
• [4] С. M. Elliott and A. M. Stuart, Viscous Cahn-Hilliard equation. II. Analysis, J. Differential Equations 128 (1996), 387-414.
• [5] С. M. Elliott and S. M. Zheng, On the Cahn-Hilliard equation, Arch. Rat. Mech. Anal. 96 (1986), 339-357.
• [6] A. A. Golovin, S. H. Davis and A. A. Nepomnyashchy, A convective Cahn-Hilliard model for the formation of facets and comers in crystal growth, Phys. D 122 (1998), 202-230.
• [7] К. H. Kwek, On the Cahn-Hilliard type equation, Doctoral Thesis, Georgia Institute of Technology, 1991.
• [8] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. II, Springer, 1972.
• [9] M. Schechter, Spectra of Partial Differential Operators, North-Holland, Amsterdam, 1986.
• [10] J. Shatah and W. Strauss, Spectral condition for instability, in: Contemp. Math. 255 (2000), 189-198.
• [11] W. Strauss and G. Wang, Instability of traveling waves of the Kuramoto-Sivashinsky equation, Chin. Ann. Math. Ser. В 23 (2002), 267-276.
• [12] S. J. Watson, F. Otto, B. Y. Rubinstein and S. H. Davis, Coarsening dynamics of the convective Cahn-Hilliard equation, Phys. D 178 (2003), 127-148.
• [13] Q. Ye and Z. Li, Theory of Reaction-Diffusion Equations, Science Press, Beijing, 1994.
• [14] J. Yin and C. Liu, Regularity of solutions of the Cahn-Hilliard equation with concentration dependent mobility, Nonlinear Anal. 45 (2001), 543-554.