메뉴 건너뛰기




Volumn 125, Issue 1, 1996, Pages 154-183

Convergence of the Cahn-Hilliard equation to the Mullins-Sekerka problem in spherical symmetry

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030577717     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0028     Document Type: Article
Times cited : (56)

References (35)
  • 2
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • N. D. ALIKAKOS, P. W. BATES, AND G. FUSCO, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eq. 90 (1991), 81-135.
    • (1991) J. Diff. Eq. , vol.90 , pp. 81-135
    • Alikakos, N.D.1    Bates, P.W.2    Fusco, G.3
  • 3
    • 0018480694 scopus 로고
    • A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
    • S. ALLEN AND J. CAHN, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall. 27 (1979), 1084-1095.
    • (1979) Acta Metall. , vol.27 , pp. 1084-1095
    • Allen, S.1    Cahn, J.2
  • 5
    • 0001636556 scopus 로고
    • On the asymptotic solution of a nonlinear Dirichlet problem
    • M. S. BERGER AND L. E. FRAENKEL, On the asymptotic solution of a nonlinear Dirichlet problem, J. Math. Mech. 19 (1970), 553-585.
    • (1970) J. Math. Mech. , vol.19 , pp. 553-585
    • Berger, M.S.1    Fraenkel, L.E.2
  • 6
    • 84971972596 scopus 로고
    • The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. Part I: Mathematical analysis
    • J. E. BLOWEY AND C. M. ELLIOTT, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy. Part I: Mathematical analysis, Euro. J. Appl. Math. 2 (1991), 223-279.
    • (1991) Euro. J. Appl. Math. , vol.2 , pp. 223-279
    • Blowey, J.E.1    Elliott, C.M.2
  • 8
    • 44949278065 scopus 로고
    • Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
    • L. BRONSARD AND R. V. KOHN, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics, J. Diff. Eq. 90 (1989), 211-237.
    • (1989) J. Diff. Eq. , vol.90 , pp. 211-237
    • Bronsard, L.1    Kohn, R.V.2
  • 9
    • 84990575560 scopus 로고
    • On the slowness of phase boundary motion in one space dimension
    • L. BRONSARD AND R. V. KOHN, On the slowness of phase boundary motion in one space dimension, Comm. Pure Appl. Math. 18 (1990), 983-997.
    • (1990) Comm. Pure Appl. Math. , vol.18 , pp. 983-997
    • Bronsard, L.1    Kohn, R.V.2
  • 10
    • 0001196888 scopus 로고
    • On the slow dynamics for the Cahn-Hilliard equation in one space dimension
    • L. BRONSARD AND D. HILHORST, On the slow dynamics for the Cahn-Hilliard equation in one space dimension, Proc. R. Soc. Lond. A 439 (1992), 669-682.
    • (1992) Proc. R. Soc. Lond. A , vol.439 , pp. 669-682
    • Bronsard, L.1    Hilhorst, D.2
  • 11
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system. I. Interfacial free energy
    • J. W. CAHN, AND J. E. HILLIARD, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958), 258-267.
    • (1958) J. Chem. Phys. , vol.28 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 12
    • 0015018902 scopus 로고
    • Spinodal decomposition: A reprise
    • J. W. CAHN, AND J. E. HILLIARD, Spinodal decomposition: a reprise, Acta Metall. 19 (1971), 151-161.
    • (1971) Acta Metall. , vol.19 , pp. 151-161
    • Cahn, J.W.1    Hilliard, J.E.2
  • 13
    • 33646973938 scopus 로고
    • Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations
    • G. CAGINALP, Stefan and Hele-Shaw type models as asymptotic limits of the phase field equations, Phys. Rev. 39 (1989), No. 11, 5887-5896.
    • (1989) Phys. Rev. , vol.39 , Issue.11 , pp. 5887-5896
    • Caginalp, G.1
  • 14
    • 85029971412 scopus 로고    scopus 로고
    • Phase field equations in the singular limit of sharp interface problems
    • G. CAGINALP, AND X. CHEN, Phase field equations in the singular limit of sharp interface problems, IMA Preprint Ser. 787 (1991).
    • IMA Preprint Ser. , vol.787 , pp. 1991
    • Caginalp, G.1    Chen, X.2
  • 16
    • 21144479953 scopus 로고
    • Hele-Shaw problem and area-preserving, curve shorting motion
    • to appear
    • X. CHEN, Hele-Shaw problem and area-preserving, curve shorting motion, ARMA, to appear, (1993).
    • (1993) ARMA
    • Chen, X.1
  • 18
    • 84990617538 scopus 로고
    • Phase transitions and generalized motion by mean curvature
    • L. C. EVANS, H. M. SONER, AND P. E. SOUGANIDIS, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45 (1991), 1097-1123.
    • (1991) Comm. Pure Appl. Math. , vol.45 , pp. 1097-1123
    • Evans, L.C.1    Soner, H.M.2    Souganidis, P.E.3
  • 19
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature
    • L. C. EVANS, AND J. SPRUCK, Motion of level sets by mean curvature, J. Diff. Geo. 33 (1991), 635-681.
    • (1991) J. Diff. Geo. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 21
    • 0001863910 scopus 로고
    • Slow-motion manifolds, dormant instabilities, and singular perturbations
    • G. FUSCO, AND J. K. HALE, Slow-motion manifolds, dormant instabilities, and singular perturbations, J. Dyn. Diff. Eq. 1 (1989), 75-94.
    • (1989) J. Dyn. Diff. Eq. , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.K.2
  • 24
    • 84971922508 scopus 로고
    • Solutions of the Two Phase Stefan Problem with the Gibbs-Thomson relation for the Melting Temperature
    • ST. LUCKHAUS, Solutions of the Two Phase Stefan Problem with the Gibbs-Thomson relation for the Melting Temperature, Euro. J. Appl. Math. 1 (1990), 101-111.
    • (1990) Euro. J. Appl. Math. , vol.1 , pp. 101-111
    • Luckhaus, S.T.1
  • 25
    • 33845220501 scopus 로고
    • The Gibbs-Thomson relation within the gradient theory for phase transitions
    • ST. LUCKHAUS, AND L. MODICA, The Gibbs-Thomson relation within the gradient theory for phase transitions, ARMA 107 (1989), 71-83.
    • (1989) ARMA , vol.107 , pp. 71-83
    • Luckhaus, S.T.1    Modica, L.2
  • 26
    • 34250109116 scopus 로고
    • Gradient theory of phase transition and singular perturbation
    • L. MODICA, Gradient theory of phase transition and singular perturbation, ARMA 98 (1986), 123-142.
    • (1986) ARMA , vol.98 , pp. 123-142
    • Modica, L.1
  • 27
    • 0001318159 scopus 로고
    • Évolution géomtrique d'interface
    • P. DE MOTTONI, AND M. SCHATZMAN, Évolution géomtrique d'interface, Comp. Rend. Paris 309 (1989), 453-458.
    • (1989) Comp. Rend. Paris , vol.309 , pp. 453-458
    • De Mottoni, P.1    Schatzman, M.2
  • 28
    • 0039088777 scopus 로고
    • Geometrical evolution of developed interfaces
    • to appear
    • P. DE MOTTONI, AND M. SCHATZMAN, Geometrical evolution of developed interfaces, Trans. AMS, to appear, 1993.
    • (1993) Trans. AMS
    • De Mottoni, P.1    Schatzman, M.2
  • 29
    • 36849117884 scopus 로고
    • Morphological stability of a particle growing by diffusion and heat flow
    • W. W. MULLINS, AND R. F. SEKERKA, Morphological stability of a particle growing by diffusion and heat flow, J. Appl. Phys. 34 (1963), 323-329.
    • (1963) J. Appl. Phys. , vol.34 , pp. 323-329
    • Mullins, W.W.1    Sekerka, R.F.2
  • 30
    • 85029965083 scopus 로고
    • Existence and uniqueness of radially symmetric stationary points within the gradient theory of phase transitions
    • to appear
    • B. S. NIETHAMMER, Existence and Uniqueness of Radially Symmetric Stationary Points within the Gradient Theory of Phase Transitions, Euro. J. Appl. Math., to appear, 1993.
    • (1993) Euro. J. Appl. Math.
    • Niethammer, B.S.1
  • 32
    • 0001410452 scopus 로고
    • Front migration in the non-linear Cahn-Hilliard equation
    • R. L. PEGO, Front migration in the non-linear Cahn-Hilliard equation, Proc. R. Soc. Lond. A 422 (1989), 261-278.
    • (1989) Proc. R. Soc. Lond. A , vol.422 , pp. 261-278
    • Pego, R.L.1
  • 35
    • 85029970431 scopus 로고
    • The Cahn-Hilliard equation as limit of the phase field equations
    • to appear
    • B. E. STOTH, The Cahn-Hilliard equation as limit of the phase field equations, Quart. Appl. Math., to appear, 1993.
    • (1993) Quart. Appl. Math.
    • Stoth, B.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.