Convergence of solutions to Cahn-Hilliard equation

Communications in Partial Differential Equations

Volumn 24, Issue 5-6, 1999, Pages 1055-1077

  Rybka, Piotr ^a,b   Hoffmann, Karl Heinz ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475056     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309908821458     Document Type: Article

References (21)

1. N. Alikakos, P.W. Bates, G. Fusco, Slow motion for Cahn-Hilliard equation in one space dimension, J. Differential Equations 90, (1991), 81-134.
2. N. Alikakos, G. Fusco, M. Kowalczyk, Finite dimensional dynamics and interfaces intersecting the boundary I, Indiana Univ. Math. J., 45, (1996), 1119-1155.
3. P. Bates, P. Fife, The dynamics of nucleation for Cahn-Hilliard equation, SIAM J. Appl. Math. 53, (1993), 990-1008.
4. X. Chen, M. Kowalczyk, Existence of equilibria for the Cahn-Hilliard equation via local minimizers of the perimeter, Comm. Partial Differential Equations, 21, (1996) 1207-1233.
5. P.C. Fife, H. Kielhöfer, S. Maier-Paape, Th. Wanner, Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation, Physica D, 100 (1997), 257-278.
6. D. Gilbarg, N.S. Trudinger, "Elliptic partial differential equations of second order". (Grundlehren Math. Wiss. Bd. 224) Berlin, Heidelberg, New York: Springer 1977 (first ed.), 1983 (second ed.)
7. C.P. Grant, Spinodal decomposition for the Cahn-Hilliard equation, Comm. Partial Differential Equations, 18, (1993), 453-490.
8. M. Grinfeld, A. Novick-Cohen, Counting stationary solutions of the Cahn-Hilliard equation by transversality argument, Proc. Roy. Soc. Edinburgh Sect. A, 125, (1995), 351-370.
9. M. Grinfeld, A. Novick-Cohen, The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor, preprint.
10. J.K. Hale, "Asymptotic behavior of dissipative systems". (Mathematical Surveys and Monographs 25) Providence: American Mathematical Society 1988
11. D. Henry, "Geometric theory of semilinear parabolic equations". (Lecture Notes in Mathematics, vol. 840) Berlin: Springer 1981. [Russian translation: Moscow: Mir 1985]
12. S. Lojasiewicz, Ensemble semi-analytic. Bures-sur-Yvette: IHES (1965)
13. S. Lojasiewicz, Une propriété topologique des sous-ensembles analytiques reéls. Colloque Internationaux du C.N.R.S. # 117, Les equations aux derivées partielles (1963), 87-89.
14. S. Lojasiewicz, Sur la geometrie semi-et sous-analytique. Ann. Inst. Fourier (Grenoble) 43, (1993), 1575-1595
15. L. Nirenberg, "Topics in Nonlinear Functional Analysis". New York: Courant Institute of Mathematical Sciences, 1974
16. P. Rybka, K.-H. Hoffmann, Convergence of solutions to the equation of quasi-static approximation of viscoelasticity with capillarity, J. Math. Anal. Appl. 226, (1998), 61-81.
17. L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. of Math. 118, (1983), 525-571
18. J. Wei, M. Winter, Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear).
19. J. Wei, M. Winter, On the stationary Cahn-Hilliard equation: interior spike solutions, J. Differential Equations 148, (1998), 231-267.
20. J. Wei, M. Winter, On the stationary Cahn-Hilliard equation: bubble solutions, SIAM J. Math. Anal, (to appear).
21. S. Zheng, Asymptotic behavior of solutions to Cahn-Hilliard equation, Appl. Anal. 23 (1986), 165-184.