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Volumn 57, Issue 5-6, 2004, Pages 843-877

Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations

Author keywords

Cahn Hilliard equations; Exponential attractor; Inertial manifold; Semiflow; Singular perturbation

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; DIFFUSION; FUNCTIONS; MATHEMATICAL MODELS;

EID: 2542500465     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.03.023     Document Type: Article
Times cited : (44)

References (27)
  • 1
    • 2542425143 scopus 로고    scopus 로고
    • Global dynamics of the viscous cahn-hilliard equations
    • An L. Global dynamics of the viscous Cahn-Hilliard equations. J. Lanzhou Univ. 36(5):2000;17-23.
    • (2000) J. Lanzhou Univ. , vol.36 , Issue.5 , pp. 17-23
    • An, L.1
  • 2
    • 2542418554 scopus 로고    scopus 로고
    • Global solutions to a generalized cahn-hilliard equation with viscosity
    • Bonetti E., Dreyer W., Schimperna G. Global solutions to a generalized Cahn-Hilliard equation with viscosity. Adv. Differential Equations. 8(2):2003;231-256.
    • (2003) Adv. Differential Equations , vol.8 , Issue.2 , pp. 231-256
    • Bonetti, E.1    Dreyer, W.2    Schimperna, G.3
  • 3
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system, I, interfacial free energy
    • Cahn J.W., Hilliard E. Free energy of a nonuniform system, I, interfacial free energy. J. Chem. Phys. 28:1958;258-367.
    • (1958) J. Chem. Phys. , vol.28 , pp. 258-367
    • Cahn, J.W.1    Hilliard, E.2
  • 5
    • 2542419522 scopus 로고
    • A singularly perturbed phase field problem. Upper semicontinuity of the attractor
    • Dupaix C., Hilhorst D. A singularly perturbed phase field problem. Upper semicontinuity of the attractor. Gakuto Int. Ser. Math. Sci. Appl. 7:1995;101-112.
    • (1995) Gakuto Int. Ser. Math. Sci. Appl. , vol.7 , pp. 101-112
    • Dupaix, C.1    Hilhorst, D.2
  • 6
    • 2542429824 scopus 로고    scopus 로고
    • The viscous Cahn-Hilliard equations as a limit of the phase field model: The lower semicontinuity of the attractors
    • Dupaix C., Hilhorst D., Kostin I.N. The viscous Cahn-Hilliard equations as a limit of the phase field model. the lower semicontinuity of the attractors J. Dyn. Differential Eqs. 11(2):1999;333-353.
    • (1999) J. Dyn. Differential Eqs. , vol.11 , Issue.2 , pp. 333-353
    • Dupaix, C.1    Hilhorst, D.2    Kostin, I.N.3
  • 8
    • 1642274906 scopus 로고    scopus 로고
    • Lower semicontinuity of a non-hyperbolic attractor for the viscous cahn-hilliard equation
    • Elliott C.M., Kostin I.K. Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation. Nonlinearity. 9(3):1996;687-702.
    • (1996) Nonlinearity , vol.9 , Issue.3 , pp. 687-702
    • Elliott, C.M.1    Kostin, I.K.2
  • 9
    • 0030187271 scopus 로고    scopus 로고
    • The viscous cahn-hilliard equation, II
    • Elliott C.M., Stuart A.M. The viscous Cahn-Hilliard equation, II. J. Differential Equations. 128(2):1996;387-414.
    • (1996) J. Differential Equations , vol.128 , Issue.2 , pp. 387-414
    • Elliott, C.M.1    Stuart, A.M.2
  • 13
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • Am. Math. Soc. Providence, RI
    • J. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys and Monographs, Vol. 25, Am. Math. Soc. Providence, RI, 1988.
    • (1988) Math. Surveys and Monographs , vol.25
    • Hale, J.1
  • 14
    • 0000610074 scopus 로고
    • Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
    • Hale J.K., Raugel G. Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation. J. Differential Equations. 73(2):1988;197-214.
    • (1988) J. Differential Equations , vol.73 , Issue.2 , pp. 197-214
    • Hale, J.K.1    Raugel, G.2
  • 15
    • 0002931112 scopus 로고
    • Lower semicontinuity of the attractor for a singularly perturbed hyperbolic equation
    • Hale J.K., Raugel G. Lower semicontinuity of the attractor for a singularly perturbed hyperbolic equation. J. Dyn. Differential Equations. 2(1):1990;19-67.
    • (1990) J. Dyn. Differential Equations , vol.2 , Issue.1 , pp. 19-67
    • Hale, J.K.1    Raugel, G.2
  • 16
    • 38249026350 scopus 로고
    • Inertial manifolds associated to partly dissipative reaction diffusion equations
    • Marion M. Inertial manifolds associated to partly dissipative reaction diffusion equations. J. Math. Anal. Appl. 143:1989;295-326.
    • (1989) J. Math. Anal. Appl. , vol.143 , pp. 295-326
    • Marion, M.1
  • 17
    • 0009903233 scopus 로고
    • Finite-dimensional attracting invariant manifolds for damped semilinear wave equations
    • I. Diaz, & P.L. Lions. Harlow: Longman, Contributions to Nonlinear PDEs, II
    • Mora X. Finite-dimensional attracting invariant manifolds for damped semilinear wave equations. Diaz I., Lions P.L. Contributions to Nonlinear PDEs, II. Pitman Research Notes on Mathematics. Vol. 155:1983;172-183 Longman, Harlow.
    • (1983) Pitman Research Notes on Mathematics , vol.155 , pp. 172-183
    • Mora, X.1
  • 18
    • 0002844740 scopus 로고
    • Existence and nonexistence of finite dimensional globally attracting invariant manifolds in semilinear damped wave equations
    • Dynamics of Infinite Dimensional Systems, Lisbon, 1986, Springer, New York
    • X. Mora, J. Solà-Morales, Existence and nonexistence of finite dimensional globally attracting invariant manifolds in semilinear damped wave equations, in: Dynamics of Infinite Dimensional Systems, Proceedings of NATO Advanced Studies Institute, Lisbon, 1986, Springer, New York, 1987, pp. 187-210.
    • (1987) Proceedings of NATO Advanced Studies Institute , pp. 187-210
    • Mora, X.1    Solà-Morales, J.2
  • 19
    • 0000520933 scopus 로고
    • Some global dynamical properties of a class of pattern formation equations
    • Nicolaenko B., Scheurer B., Temam R. Some global dynamical properties of a class of pattern formation equations. Commun. PDEs. 14:1989;245-297.
    • (1989) Commun. PDEs , vol.14 , pp. 245-297
    • Nicolaenko, B.1    Scheurer, B.2    Temam, R.3
  • 21
    • 0007322095 scopus 로고
    • Steady states of the one-dimensional cahn-hilliard equation
    • A. Novick-Cohen, L. Peletier, Steady states of the one-dimensional Cahn-Hilliard equation, Proc. Royal Soc. Edinburgh, Sct. A, vol. 123/6, (1993), pp. 1071-1098.
    • (1993) Proc. Royal Soc. Edinburgh, Sct. A , vol.123 , Issue.6 , pp. 1071-1098
    • Novick-Cohen, A.1    Peletier, L.2
  • 22
    • 0003648426 scopus 로고    scopus 로고
    • Infinite dimensional dynamical systems. An introduction to dissipative parabolic pdes and the theory of global attractors
    • Cambridge: Cambridge University Press
    • C. Robinson J. Infinite Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics. 2001;Cambridge University Press, Cambridge.
    • (2001) Cambridge Texts in Applied Mathematics
    • Robinson, J.C.1
  • 23
    • 0033475056 scopus 로고    scopus 로고
    • Convergence of solutions to cahn-hilliard equation
    • Rybka P., Hoffmann K-H. Convergence of solutions to Cahn-Hilliard equation. Commun. PDE. 24(5, 6):1999;1055-1077.
    • (1999) Commun. PDE , vol.24 , Issue.5-6 , pp. 1055-1077
    • Rybka, P.1    Hoffmann, K.-H.2
  • 26
    • 84972948188 scopus 로고
    • Asymptotic behavior of solutions to the cahn-hilliard equation
    • Zheng S. Asymptotic behavior of solutions to the Cahn-Hilliard equation. Appl. Anal. 3:1986;165-184.
    • (1986) Appl. Anal. , vol.3 , pp. 165-184
    • Zheng, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.