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Volumn 2, Issue 3, 2001, Pages 273-304

Long-time behavior of some models of Cahn-Hilliard equations in deformable continua

Author keywords

Attractor; Deformable continuum; Exponential attractor; Generalized Cahn Hilliard equation; Squeezing property; Uniform attractor

Indexed keywords


EID: 0035457838     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(00)00104-8     Document Type: Article
Times cited : (30)

References (30)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of partial differential equations satisfying general boundary conditions I, II
    • S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math. 12, (1959) 623-727; 17 (1964) 35-92.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 84980080664 scopus 로고
    • S. Agmon, A. Douglis, L. Nirenberg, Estimates near the boundary for solutions of partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math. 12, (1959) 623-727; 17 (1964) 35-92.
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 35-92
  • 3
    • 0000110024 scopus 로고
    • Exponential attractors of reaction-diffusion systems in an unbounded domain
    • A. Babin, B. Nicolaenko, Exponential attractors of reaction-diffusion systems in an unbounded domain, J. Dynamics Differential Equations 7 (4) (1995) 567-590.
    • (1995) J. Dynamics Differential Equations , vol.7 , Issue.4 , pp. 567-590
    • Babin, A.1    Nicolaenko, B.2
  • 5
    • 43449102981 scopus 로고
    • On spinodal decomposition
    • J.W. Cahn, On spinodal decomposition, Acta Metall. 9 (1961) 795-801.
    • (1961) Acta Metall. , vol.9 , pp. 795-801
    • Cahn, J.W.1
  • 6
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system I, interfacial free energy
    • J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system I, interfacial free energy, J. Chem. Phys. 2 (1958) 258-267.
    • (1958) J. Chem. Phys. , vol.2 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 7
    • 0007288046 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation for an isotropic deformable continuum
    • M. Carrive, A. Miranville, A. Piétrus, J.M. Rakotoson, The Cahn-Hilliard equation for an isotropic deformable continuum, Appl. Math. Lett. 12 (2) (1999) 23-28.
    • (1999) Appl. Math. Lett. , vol.12 , Issue.2 , pp. 23-28
    • Carrive, M.1    Miranville, A.2    Piétrus, A.3    Rakotoson, J.M.4
  • 9
    • 0001530660 scopus 로고
    • Attractors of nonautonomous dynamical systems and their dimension
    • V.V. Chepyzhov, M.I. Vishik, Attractors of nonautonomous dynamical systems and their dimension, J. Math. Pure Appl. 73 (1994) 279-333.
    • (1994) J. Math. Pure Appl. , vol.73 , pp. 279-333
    • Chepyzhov, V.V.1    Vishik, M.I.2
  • 11
    • 84971744475 scopus 로고
    • Global attractors of the Cahn-Hilliard system
    • J.W. Cholewe, T. Dlotko, Global attractors of the Cahn-Hilliard system, Bull. Austral. Math. Soc. 49 (1994) 277-302.
    • (1994) Bull. Austral. Math. Soc. , vol.49 , pp. 277-302
    • Cholewe, J.W.1    Dlotko, T.2
  • 12
    • 0029307671 scopus 로고
    • On the Cahn-Hilliard equation with a logarithmic free energy
    • A. Debussche, L. Dettori, On the Cahn-Hilliard equation with a logarithmic free energy, Nonlinear Anal. TMA 24 (10) (1995) 1491-1514.
    • (1995) Nonlinear Anal. TMA , vol.24 , Issue.10 , pp. 1491-1514
    • Debussche, A.1    Dettori, L.2
  • 13
    • 3142780340 scopus 로고    scopus 로고
    • Upper-semicontinuity of the attractor for a singularly perturbed phase-field model
    • to appear
    • C. Dupaix, D. Hilhorst, Ph. Laurençot, Upper-semicontinuity of the attractor for a singularly perturbed phase-field model, Adv. Math. Sci. Appl., to appear.
    • Adv. Math. Sci. Appl.
    • Dupaix, C.1    Hilhorst, D.2    Laurençot, P.3
  • 17
    • 0032391989 scopus 로고    scopus 로고
    • Exponential attractors for nonautonomous first-order evolution equations
    • P. Fabrie, A. Miranville, Exponential attractors for nonautonomous first-order evolution equations, Discrete Control Dynamics Systems 4 (2) (1998) 225-240.
    • (1998) Discrete Control Dynamics Systems , vol.4 , Issue.2 , pp. 225-240
    • Fabrie, P.1    Miranville, A.2
  • 18
    • 0007153242 scopus 로고    scopus 로고
    • Thèse, Université Bordeaux - I
    • C. Galusinski, Thèse, Université Bordeaux - I 1996.
    • (1996)
    • Galusinski, C.1
  • 19
    • 0007286185 scopus 로고    scopus 로고
    • Exponential attractors for nonautonomous partially dissipative equations
    • C. Galusinski, M. Hnid, A. Miranville, Exponential attractors for nonautonomous partially dissipative equations, Differential Integral Equations 12 (1) (1999) 1-22.
    • (1999) Differential Integral Equations , vol.12 , Issue.1 , pp. 1-22
    • Galusinski, C.1    Hnid, M.2    Miranville, A.3
  • 20
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92 (1996) 178-192.
    • (1996) Physica D , vol.92 , pp. 178-192
    • Gurtin, M.1
  • 23
    • 0007284320 scopus 로고    scopus 로고
    • Global attractor for the Cahn-Hilliard system with fast growing nonlinearity
    • D. Li, C. Zhong, Global attractor for the Cahn-Hilliard system with fast growing nonlinearity, J. Differential Equations 149 (2) (1998) 191-210.
    • (1998) J. Differential Equations , vol.149 , Issue.2 , pp. 191-210
    • Li, D.1    Zhong, C.2
  • 24
    • 0003008783 scopus 로고    scopus 로고
    • Exponential attractors for nonautonomous evolution equations
    • A. Miranville, Exponential attractors for nonautonomous evolution equations, Appl. Math. Lett. 11 (2) (1998) 19-22.
    • (1998) Appl. Math. Lett. , vol.11 , Issue.2 , pp. 19-22
    • Miranville, A.1
  • 25
    • 0032615505 scopus 로고    scopus 로고
    • Exponential attractors for a class of evolution equations by a decomposition method
    • A. Miranville, Exponential attractors for a class of evolution equations by a decomposition method, C.R. Acad. Sci. Série I 328 (2) (1999) 145-150.
    • (1999) C.R. Acad. Sci. Série I , vol.328 , Issue.2 , pp. 145-150
    • Miranville, A.1
  • 26
    • 0000884594 scopus 로고    scopus 로고
    • A model of Cahn-Hilliard equation based on a microforce balance
    • A. Miranville, A model of Cahn-Hilliard equation based on a microforce balance, C.R. Acad. Sci. Série I 328 (12) (1999) 1247-1252.
    • (1999) C.R. Acad. Sci. Série I , vol.328 , Issue.12 , pp. 1247-1252
    • Miranville, A.1
  • 27
    • 0000161026 scopus 로고    scopus 로고
    • Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance
    • A. Miranville, A. Piétrus, J.M. Rakotoson, Dynamical aspect of a generalized Cahn-Hilliard equation based on a microforce balance, Asymptotic Anal. 16 (1998) 315-345.
    • (1998) Asymptotic Anal. , vol.16 , pp. 315-345
    • Miranville, A.1    Piétrus, A.2    Rakotoson, J.M.3
  • 28
    • 0000520933 scopus 로고
    • Some global dynamical properties of a class of pattern formation equations
    • B. Nicolaenko, B. Scheurer, R. Temam, Some global dynamical properties of a class of pattern formation equations, Comm. Partial Differential Equations 14 (2) (1989) 245-297.
    • (1989) Comm. Partial Differential Equations , vol.14 , Issue.2 , pp. 245-297
    • Nicolaenko, B.1    Scheurer, B.2    Temam, R.3
  • 29
    • 0001386608 scopus 로고
    • Nonlinear aspects of the Cahn-Hilliard equation
    • A. Novick-Cohen, L.A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D 10 (1984) 277-298.
    • (1984) Physica D , vol.10 , pp. 277-298
    • Novick-Cohen, A.1    Segel, L.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.