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Volumn 44, Issue 1, 2001, Pages 33-57

Slow motion in higher-order systems and Γ-convergence in one space dimension

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; MATHEMATICAL MODELS; PHASE SEPARATION; THEOREM PROVING; VARIATIONAL TECHNIQUES;

EID: 0035284242     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00245-X     Document Type: Article
Times cited : (11)

References (46)
  • 1
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • Alikakos N.D., Bates P.W., Fusco G. Slow motion for the Cahn-Hilliard equation in one space dimension. J. Differential Equations. 90:1991;81-135.
    • (1991) J. Differential Equations , vol.90 , pp. 81-135
    • Alikakos, N.D.1    Bates, P.W.2    Fusco, G.3
  • 2
    • 0039038879 scopus 로고
    • Equilibrium and dynamics of bubbles for the Cahn-Hilliard equation
    • (Barcelona
    • N.D. Alikakos, G. Fusco, Equilibrium and dynamics of bubbles for the Cahn-Hilliard equation, in International Conference on Differential Equations, Vol. 1 (Barcelona, 1991 ), 1993, pp. 59-67.
    • (1991) In International Conference on Differential Equations , vol.1 , pp. 59-67
    • Alikakos, N.D.1    Fusco, G.2
  • 3
    • 84963254790 scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. Part I: Spectral estimates
    • Alikakos N.D., Fusco G. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. Part I: Spectral estimates. Commun. Partial Differential Equations. 19:1994;1397-1447.
    • (1994) Commun. Partial Differential Equations , vol.19 , pp. 1397-1447
    • Alikakos, N.D.1    Fusco, G.2
  • 4
    • 0032397594 scopus 로고    scopus 로고
    • Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: The motion of bubbles
    • Alikakos N.D., Fusco G. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: the motion of bubbles. Arch. Rational Mech. Anal. 141:1998;1-61.
    • (1998) Arch. Rational Mech. Anal. , vol.141 , pp. 1-61
    • Alikakos, N.D.1    Fusco, G.2
  • 6
    • 0013197527 scopus 로고    scopus 로고
    • Transition layer solutions of a higher order equation in an infinite tube
    • Bates P.W., Ren X. Transition layer solutions of a higher order equation in an infinite tube. Commun. Partial Differential Equations. 21:1996;195-220.
    • (1996) Commun. Partial Differential Equations , vol.21 , pp. 195-220
    • Bates, P.W.1    Ren, X.2
  • 7
    • 43949159714 scopus 로고
    • Metastable patterns for the Cahn-Hilliard equation, I
    • Bates P.W., Xun J. Metastable patterns for the Cahn-Hilliard equation, I. J. Differential Equations. 111:1994;421-457.
    • (1994) J. Differential Equations , vol.111 , pp. 421-457
    • Bates, P.W.1    Xun, J.2
  • 8
    • 58149367746 scopus 로고
    • Metastable patterns for the Cahn-Hilliard equation, II, Layer dynamics and slow invariant manifold
    • Bates P.W., Xun J. Metastable patterns for the Cahn-Hilliard equation, II, Layer dynamics and slow invariant manifold. J. Differential Equations. 117:1995;165-216.
    • (1995) J. Differential Equations , vol.117 , pp. 165-216
    • Bates, P.W.1    Xun, J.2
  • 10
    • 0001196888 scopus 로고
    • On the slow dynamics for the Cahn-Hilliard equation in one space dimension
    • Bronsard L., Hilhorst D. On the slow dynamics for the Cahn-Hilliard equation in one space dimension. Proc. Roy. Soc. London, Ser. A. 439:1992;669-682.
    • (1992) Proc. Roy. Soc. London, Ser. a , vol.439 , pp. 669-682
    • Bronsard, L.1    Hilhorst, D.2
  • 11
    • 84990575560 scopus 로고
    • On the slowness of phase boundary motion in one space dimension
    • Bronsard L., Kohn R.V. On the slowness of phase boundary motion in one space dimension. Commun. Pure Appl. Math. 43:1990;983-997.
    • (1990) Commun. Pure Appl. Math. , vol.43 , pp. 983-997
    • Bronsard, L.1    Kohn, R.V.2
  • 12
    • 21344488703 scopus 로고
    • On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
    • Bronsard L., Reitich F. On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation. Arch. Rational Mech. Anal. 124:1993;355-379.
    • (1993) Arch. Rational Mech. Anal. , vol.124 , pp. 355-379
    • Bronsard, L.1    Reitich, F.2
  • 15
    • 0039088725 scopus 로고
    • J. Carr, R.L. Pego, Very slow phase separation in one dimension, in PDEs and continuum models of phase transitions (Nice, 1988 ), Lecture Notes in Physics, Vol. 344, 1989, pp. 216-226.
    • (1989) Lecture Notes in Physics , vol.344 , pp. 216-226
  • 18
    • 0000689240 scopus 로고
    • Bistable systems with propagating front leading to pattern formation
    • Dee G.T., van Saarloos W. Bistable systems with propagating front leading to pattern formation. Phys. Rev. Lett. 60:1988;2641-2644.
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 2641-2644
    • Dee, G.T.1    Van Saarloos, W.2
  • 19
    • 0001617217 scopus 로고
    • Numerical studies of the Cahn-Hilliard equation for phase separation
    • Elliott C.M., French D.A. Numerical studies of the Cahn-Hilliard equation for phase separation. IMA J. Appl. Math. 38:1987;97-128.
    • (1987) IMA J. Appl. Math. , vol.38 , pp. 97-128
    • Elliott, C.M.1    French, D.A.2
  • 20
    • 0000700422 scopus 로고
    • An analysis of numerical approximations of metastable solutions of the bistable equation
    • Estep D.J. An analysis of numerical approximations of metastable solutions of the bistable equation. Nonlinearity. 7:1994;1445-1462.
    • (1994) Nonlinearity , vol.7 , pp. 1445-1462
    • Estep, D.J.1
  • 22
    • 0030501540 scopus 로고    scopus 로고
    • Accurate parallel integration of large sparse systems of differential equations
    • Estep D.J., Williams R.D. Accurate parallel integration of large sparse systems of differential equations. Math. Models Meth. Appl. Sci. 6:1996;535-568.
    • (1996) Math. Models Meth. Appl. Sci. , vol.6 , pp. 535-568
    • Estep, D.J.1    Williams, R.D.2
  • 23
    • 84975994718 scopus 로고
    • The gradient theory of phase transitions for systems with two potential wells
    • Fonseca I., Tartar L. The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh. 111A:1989;89-102.
    • (1989) Proc. Roy. Soc. Edinburgh , vol.111 , pp. 89-102
    • Fonseca, I.1    Tartar, L.2
  • 24
    • 0040731158 scopus 로고
    • Limit theorems for large deviations and reaction-diffusion equations
    • Freidlin M.I. Limit theorems for large deviations and reaction-diffusion equations. Ann. Probab. 13:1985;639-675.
    • (1985) Ann. Probab. , vol.13 , pp. 639-675
    • Freidlin, M.I.1
  • 25
    • 0022699402 scopus 로고
    • Geometric optics approach to reaction-diffusion equations
    • Freidlin M.I. Geometric optics approach to reaction-diffusion equations. SIAM J. Appl. Math. 46:1986;222-232.
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 222-232
    • Freidlin, M.I.1
  • 26
    • 0003089849 scopus 로고
    • xx + f(u) for small ε
    • Stuttgart
    • xx + f(u) for small ε . in Problems involving change of type (Stuttgart, 1988 ), Lecture Notes in Physics, Vol. 359, 1990, pp. 53-73.
    • (1988) In Problems Involving Change of Type
    • Fusco, G.1
  • 27
    • 0343335448 scopus 로고
    • xx + f(u) for small ε . in Problems involving change of type (Stuttgart, 1988 ), Lecture Notes in Physics, Vol. 359, 1990, pp. 53-73.
    • (1990) Lecture Notes in Physics , vol.359 , pp. 53-73
  • 28
    • 0001863910 scopus 로고
    • Slow-motion manifolds, dormant instability, and singular perturbations
    • Fusco G., Hale J.K. Slow-motion manifolds, dormant instability, and singular perturbations. J. Dyn. Differential Equations. 1:1989;75-94.
    • (1989) J. Dyn. Differential Equations , vol.1 , pp. 75-94
    • Fusco, G.1    Hale, J.K.2
  • 30
    • 0040619949 scopus 로고
    • Slow motion in one-dimensional Cahn-Morral systems, SIAM
    • Grant C.P. Slow motion in one-dimensional Cahn-Morral systems, SIAM. J. Math. Anal. 26:1995;21-34.
    • (1995) J. Math. Anal. , vol.26 , pp. 21-34
    • Grant, C.P.1
  • 31
    • 0011341090 scopus 로고
    • Slowly-migrating transition layers for the discrete Allen-Cahn and Cahn-Hilliard equations
    • Grant C.P., Van Vleck E.S. Slowly-migrating transition layers for the discrete Allen-Cahn and Cahn-Hilliard equations. Nonlinearity. 8:1995;861-876.
    • (1995) Nonlinearity , vol.8 , pp. 861-876
    • Grant, C.P.1    Van Vleck, E.S.2
  • 33
    • 0010134617 scopus 로고
    • On the slow motions of phase boundaries in the Korteweg theory of capillarity
    • Hattori H., Mischaikow K. On the slow motions of phase boundaries in the Korteweg theory of capillarity. Dyn. Systems Appl. 1:1992;441-452.
    • (1992) Dyn. Systems Appl. , vol.1 , pp. 441-452
    • Hattori, H.1    Mischaikow, K.2
  • 34
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer, Berlin, 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 35
    • 0032478448 scopus 로고    scopus 로고
    • Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
    • Kalies W.D., Kwapisz J., VanderVorst R.C. Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria. Commun. Math. Phys. 193:1998;337-371.
    • (1998) Commun. Math. Phys. , vol.193 , pp. 337-371
    • Kalies, W.D.1    Kwapisz, J.2    Vandervorst, R.C.3
  • 36
    • 0030295224 scopus 로고    scopus 로고
    • Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation
    • Kalies W.D., VanderVorst R.C. Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation. J. Differential Equations. 131:1996;209-228.
    • (1996) J. Differential Equations , vol.131 , pp. 209-228
    • Kalies, W.D.1    Vandervorst, R.C.2
  • 37
    • 34250109116 scopus 로고
    • The gradient theory of phase transitions and the minimal interface criterion
    • Modica L. The gradient theory of phase transitions and the minimal interface criterion. Arc. Rational Mech. Anal. 98:1987;123-142.
    • (1987) Arc. Rational Mech. Anal. , vol.98 , pp. 123-142
    • Modica, L.1
  • 38
    • 33845222258 scopus 로고    scopus 로고
    • Nonconvex variational problems with general singular perturbations
    • Owen N.C. Nonconvex variational problems with general singular perturbations. Trans. Amer. Math. Soc. 310:1998;393-404.
    • (1998) Trans. Amer. Math. Soc. , vol.310 , pp. 393-404
    • Owen, N.C.1
  • 40
    • 85037775971 scopus 로고
    • Periodic and heteroclinic orbits for a periodic Hamiltonian system
    • Rabinowitz P.H. Periodic and heteroclinic orbits for a periodic Hamiltonian system. Ann. l'Inst. Henri Poincaré. Anal. Non Linéaire. 6(5):1989;331-346.
    • (1989) Ann. l'Inst. Henri Poincaré. Anal. Non Linéaire , vol.6 , Issue.5 , pp. 331-346
    • Rabinowitz, P.H.1
  • 42
    • 0003258073 scopus 로고
    • Metastable internal layer dynamics for the viscous Cahn-Hilliard equation
    • Reyna L.G., Ward M.J. Metastable internal layer dynamics for the viscous Cahn-Hilliard equation. Meth. Appl. Anal. 2:1995;285-306.
    • (1995) Meth. Appl. Anal. , vol.2 , pp. 285-306
    • Reyna, L.G.1    Ward, M.J.2
  • 44
    • 34250095380 scopus 로고    scopus 로고
    • The effect of a singular perturbation on nonconvex variational problems
    • Sternberg P. The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101:1998;209-260.
    • (1998) Arch. Rational Mech. Anal. , vol.101 , pp. 209-260
    • Sternberg, P.1
  • 45
    • 0000482727 scopus 로고
    • Vector-valued local minimizers of nonconvex variational problems
    • Sternberg P. Vector-valued local minimizers of nonconvex variational problems. Rocky Mountain J. Math. 21:1991;799-807.
    • (1991) Rocky Mountain J. Math. , vol.21 , pp. 799-807
    • Sternberg, P.1
  • 46
    • 0002850821 scopus 로고
    • The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation in density
    • van der Waals J.D. The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation in density. Verh. Konink. Akad. Wetensch. Amsterdam. 1:1893;1-56.
    • (1893) Verh. Konink. Akad. Wetensch. Amsterdam , vol.1 , pp. 1-56
    • Van Der Waals, J.D.1


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