Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation

Nonlinearity

Volumn 9, Issue 3, 1996, Pages 687-702

  Elliott, C M ^a   Kostin, I N ^b  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642274906     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/9/3/005     Document Type: Article

References (27)

1. Babin A V and Vishik M I 1986 Unstable invariant manifolds of semigroups of nonlinear operators and their perturbations Usp. Mat. Nauk/ 41
2. (Engl. transl. Russian Math. Surveys 41(4) (1986) 1-41)
3. Babin A V and Vishik M I 1992 Attractors of Evolution Equations (Amsterdam: North Holland)
4. Bai F, Elliott C M, Gardiner A, Spence A and Stuart A M 1995 The Viscous Cahn-Hilliard equation. Part 1: Computations Nonlinearity 8 131-60
5. Chafee N and Infante E F 1974 A bifurcation problem for a nonlinear parabolic equation J. Appl. Anal. 4 17-37
6. Elliott C M and Stuart A M 1996 The Viscous Cahn-Hilliard equation. Part 2 J. Diff. Eq. in press
7. Hale J K 1988 Asymptotic behavior of dissipative systems Math. Surveys Monographs vol 25 (Providence, RI: Am. Math. Soc.)
8. Hale J K, Lin X B and Raugel G 1988 Upper-semicontinuity of attractors for approximations of semigroups and partial differential equations Math. Comput. 5 89-123
9. Hale J K and Raugel G 1989 Lower-semicontinuity of attractors of gradient systems and applications Ann. Math. Pura Appl. 154 281-326
10. Henry D 1981 Geometric theory of semilinear parabolic equations Lecture Notes in Math. vol 840 (Berlin: Springer)
11. Henry D 1985 Some infinite dimensional Morse-Smale systems defined by parabolic differential equations J. Diff. Eq. 59 165-205
12. Hirsch M, Pugh C and Shub M 1977 Invariant manifolds Lecture Notes in Math. vol 583 (Berlin: Springer)
13. Humphries A R 1993 Numerical analysis of dynamical systems PhD thesis University of Bath
14. Kapitanskii L V and Kostin I N 1990 Attractors of nonlinear evolution equations and their approximations Algebra i Analiz 2
15. (Engl. transl. Leningrad Math. J. 2(1) (1991) 97-117)
16. Kostin I N 1990 A regular approach to a problem on the attractors of singularly perturbed equations Zap. Nauchn. Semin. LOMI 181
17. (Engl. transl. J. Sov. Math. 62 (1992) 2664-89)
18. Kostin I N 1995 Lower semicontinuity of a non-hyperbolic attractor J. London Math. Soc. 52 568-82
19. Ladyzhenskaya O A 1987 On determination of minimal global attractors for the Navier-Stokes equations and other partial differential equations Usp. Mat. Nauk 42
20. (Engl. transl. Russian Math. Surveys 42(6) 27-73)
21. Ladyzhenskaya O A 1991 Attractors for Semigroups and Evolution Equations (Cambridge: Cambridge University Press)
22. Ladyzhenskaya O A 1992 Some complements and corrections to my papers on the theory of attractors for abstract semigroups J. Sov. Math. 62 2789-94
23. Mallet-Paret J and Sell G R 1988 Inertial manifolds for reaction-diffusion equations in higher space dimensions J. Am. Math. Soc. 1 805-64
24. Novick-Cohen A 1988 On the viscous Cahn-Hilliard equation Material Instabilities in continuum and related mathematical problems ed J M Ball pp 329-42
25. Stuart A 1994 Numerical analysis of dynamical systems Acta Numerica 1994, 467-572 (Cambridge: Cambridge University Press)
26. Temam R 1988 Infinite-dimensional dynamical systems in mechanics and physics Appl. Math. Sci. vol 68 (Berlin: Springer)
27. Wells J C 1976 Invariant manifolds of nonlinear operators Pacific J. Math. 62 285-93