메뉴 건너뛰기




Volumn 151, Issue 3, 2000, Pages 187-219

Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0040191753     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050196     Document Type: Article
Times cited : (70)

References (31)
  • 1
    • 84980075953 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions
    • S. AGMON, A. DOUGLIS & L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Communications on Pure and Applied Mathematics 12, 623-727, 1959.
    • (1959) I. Communications on Pure and Applied Mathematics , vol.12 , pp. 623-727
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 2
    • 84980080664 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions
    • S. AGMON, A. DOUGLIS & L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Communications on Pure and Applied Mathematics 17, 35-92, 1964.
    • (1964) II. Communications on Pure and Applied Mathematics , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 3
    • 0032397594 scopus 로고    scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
    • N. D. ALIKAKOS & G. FUSCO, Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles. Archive for Rational Mechanics and Analysis 141, 1-61, 1998.
    • (1998) Archive for Rational Mechanics and Analysis , vol.141 , pp. 1-61
    • Alikakos, N.D.1    Fusco, G.2
  • 5
    • 0001038494 scopus 로고    scopus 로고
    • Integral manifolds for Carathéodory type differential equations in Banach spaces
    • B. AULBACH & F. COLONIUS, editors, World Scientific
    • B. AULBACH & T. WANNER, Integral manifolds for Carathéodory type differential equations in Banach spaces. In Six Lectures on Dynamical Systems, B. AULBACH & F. COLONIUS, editors, pages 45-119. World Scientific, 1996.
    • (1996) Six Lectures on Dynamical Systems , pp. 45-119
    • Aulbach, B.1    Wanner, T.2
  • 6
    • 0041016678 scopus 로고    scopus 로고
    • Invariant foliations for Carathéodory type differential equations in Banach spaces
    • B. AULBACH & T. WANNER, Invariant foliations for Carathéodory type differential equations in Banach spaces. Preprint, 1998.
    • (1998) Preprint
    • Aulbach, B.1    Wanner, T.2
  • 8
    • 0002538743 scopus 로고
    • Invariant manifolds for semilinear partial differential equations
    • U. KIRCHGRABER & H.-O. WALTHER, editors, B. G. Teubner and John Wiley & Sons
    • P. W. BATES & C. K. JONES, Invariant manifolds for semilinear partial differential equations. In Dynamics Reported, volume 2, U. KIRCHGRABER & H.-O. WALTHER, editors, pages 1-38. B. G. Teubner and John Wiley & Sons, 1989.
    • (1989) Dynamics Reported , vol.2 , pp. 1-38
    • Bates, P.W.1    Jones, C.K.2
  • 9
    • 36849125304 scopus 로고
    • Free energy of a nonuniform system. II. Thermodynamic basis
    • J. W. CAHN, Free energy of a nonuniform system. II. Thermodynamic basis. Journal of Chemical Physics 30, 1121-1124, 1959.
    • (1959) Journal of Chemical Physics , vol.30 , pp. 1121-1124
    • Cahn, J.W.1
  • 10
    • 0343909968 scopus 로고
    • Phase separation by spinodal decomposition in isotropic systems
    • J. W. CAHN, Phase separation by spinodal decomposition in isotropic systems. Journal of Chemical Physics 42, 93-99, 1965.
    • (1965) Journal of Chemical Physics , vol.42 , pp. 93-99
    • Cahn, J.W.1
  • 12
    • 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. Journal of Chemical Physics 28, 258-267, 1958.
    • (1958) Journal of Chemical Physics , vol.28 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 13
    • 38149145802 scopus 로고
    • Smooth invariant foliations in infinite dimensional spaces
    • S.-N. CHOW, X.-B. LIN & K. LU, Smooth invariant foliations in infinite dimensional spaces. Journal of Differential Equations 94, 266-291, 1991.
    • (1991) Journal of Differential Equations , vol.94 , pp. 266-291
    • Chow, S.-N.1    Lin, X.-B.2    Lu, K.3
  • 15
    • 38249029133 scopus 로고
    • Invariant manifolds for flows in Banach spaces
    • S.-N. CHOW & K. LU, Invariant manifolds for flows in Banach spaces. Journal of Differential Equations 74, 285-317, 1988.
    • (1988) Journal of Differential Equations , vol.74 , pp. 285-317
    • Chow, S.-N.1    Lu, K.2
  • 17
    • 0001113140 scopus 로고
    • Role of nonlinearities in off-critical quenches as described by the Cahn-Hilliard model of phase separation
    • K. R. ELDER & R. C. DESAI, Role of nonlinearities in off-critical quenches as described by the Cahn-Hilliard model of phase separation. Physical Review B 40, 243-254, 1989.
    • (1989) Physical Review B , vol.40 , pp. 243-254
    • Elder, K.R.1    Desai, R.C.2
  • 18
    • 0001653629 scopus 로고
    • Early stages of spinodal decomposition for the Cahn-Hilliard-Cook model of phase separation
    • K. R. ELDER, T. M. ROGERS & R. C. DESAI, Early stages of spinodal decomposition for the Cahn-Hilliard-Cook model of phase separation. Physical Review B 38, 4725-4739, 1988.
    • (1988) Physical Review B , vol.38 , pp. 4725-4739
    • Elder, K.R.1    Rogers, T.M.2    Desai, R.C.3
  • 19
    • 0003174115 scopus 로고    scopus 로고
    • Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation
    • P. C. FIFE, H. KIELHÖFER, S. MAIER-PAAPE & T. WANNER, Perturbation of doubly periodic solution branches with applications to the Cahn-Hilliard equation. Physica D 100, 257-278, 1997.
    • (1997) Physica D , vol.100 , pp. 257-278
    • Fife, P.C.1    Kielhöfer, H.2    Maier-Paape, S.3    Wanner, T.4
  • 25
    • 0040238767 scopus 로고    scopus 로고
    • Solutions of nonlinear planar elliptic problems with triangle symmetry
    • S. MAIER-PAAPE & T. WANNER, Solutions of nonlinear planar elliptic problems with triangle symmetry. Journal of Differential Equations 136, 1-34, 1997.
    • (1997) Journal of Differential Equations , vol.136 , pp. 1-34
    • Maier-Paape, S.1    Wanner, T.2
  • 26
    • 0032474671 scopus 로고    scopus 로고
    • Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Part I: Probability and wavelength estimate
    • S. MAIER-PAAPE & T. WANNER, Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions. Part I: Probability and wavelength estimate. Communications in Mathematical Physics 195, 435-464, 1998.
    • (1998) Communications in Mathematical Physics , vol.195 , pp. 435-464
    • Maier-Paape, S.1    Wanner, T.2
  • 27
    • 0040422570 scopus 로고
    • Inertial manifold for the Cahn-Hilliard model of phase transition
    • B. D. SLEEMAN & R. J. JARVIS, editors, Pitman
    • B. NICOLAENKO, B. SCHEURER & R. TEMAM, Inertial manifold for the Cahn-Hilliard model of phase transition. In B. D. SLEEMAN & R. J. JARVIS, editors, Ordinary and Partial Differential Equations (Dundee, 1986), pages 147-160. Pitman, 1987.
    • (1987) Ordinary and Partial Differential Equations (Dundee, 1986) , pp. 147-160
    • Nicolaenko, B.1    Scheurer, B.2    Temam, R.3
  • 29
    • 84966220887 scopus 로고
    • Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations
    • S. RANKIN III, Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations. Transactions of the American Mathematical Society 336, 523-535, 1993.
    • (1993) Transactions of the American Mathematical Society , vol.336 , pp. 523-535
    • Rankin S. III1
  • 31
    • 0011618959 scopus 로고
    • Linearization of random dynamical systems
    • C. K. JONES, U. KIRCHGRABER, & H.-O. WALTHER, editors, Springer-Verlag
    • T. WANNER, Linearization of random dynamical systems. In C. K. JONES, U. KIRCHGRABER, & H.-O. WALTHER, editors, Dynamics Reported, volume 4, pages 203-269. Springer-Verlag, 1995.
    • (1995) Dynamics Reported , vol.4 , pp. 203-269
    • Wanner, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.