Slow motion in the gradient theory of phase transitions via energy and spectrum

Calculus of Variations and Partial Differential Equations

Volumn 6, Issue 1, 1997, Pages 39-66

  Alikakos, N D ^a   Bronsard, L ^b   Fusco, G ^c,d  

^a UNIVERSITY OF TENNESSEE   (United States)

^b MCMASTER UNIVERSITY   (Canada)

^c UNIVERSITY OF L'AQUILA   (Italy)

^d UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347061352     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050081     Document Type: Article

References (31)

1. [ABCh] Alikakos, N.D., Bates, P.W., Chen Xinfu: Convergence of the Cahn-Hilliard Equation to the Hele-Shaw Model. Arch. Rational Mech. Anal. 128 (1994), 165-205
2. [ABF] Alikakos, N.D., Bates, P.W., Fusco, G. Slow motion for the Cahn-Hilliard equation in one space dimension. JDE 90 (1991), 81-135
3. [ABChF] Alikakos, N.D., Bates, P.W., Xinfu, Chen, Fusco, G. Hele-Shaw Motion of Small "drops" attached to a fixed boundary. In preparation
4. [AChF] Alikakos, N.D., Chen Xinfu, Fusco, G. The dynamics of an infinitesimal drop in the Cahn-Hilliard and related models. In preparation
5. [AF] Alikakos, N.D., Fusco, G. Proceedings of Conference in honor of W. Oliva, to appear
6. [AF1] Alikakos, N.D., Fusco, G. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. Part I: Spectral estimates. Comm. Part. Diff. Equal. 19 (1994), 1397-1447
7. [AF2] Alikakos, N.D., Fusco, G. Slow dynamics for the Cahn-Hilliard equation in higher space dimensions. Part II: The motion of bubbles; Arch. Rational Mech. Anal. To appear
8. [BF] Bates, P.W., Fife, P. The dynamics of nucleation for the Cahn-Hilliard equation. SIAM J. Appl. Math. 53 (1993), 990-1008
9. [BX1] Bates, P.W., Xun, J. Metastable patterns for the Cahn-Hilliard equation. Part I. JDE, to appear
10. [BX2] Bates, P.W., Xun, J. Metastable patterns for the Cahn-Hilliard equation. Part II, Layer dynamics and slow invariant manifold. JDE (1994)
11. [BrK] Bronsard, L., Kohn, R.V.: On the slowness of phase boundary motion in one space dimension. Comm. Pure Appl. Math. XLIII (1990), 983-997
12. [BrH] Bronsard, L., Hilhorst, D. On the slow dynamics for the Cahn-Hilliard equation in one space dimension. Proc. R. Soc. London A 439 (1992), 669-682
13. [C1] Cahn, J.W. On spinodal decomposition. Acta Metallurgica 9 (1961), 795-801
14. [C2] Cahn, J.W. Spinodal decomposition. Trans Metallurg. Soc. of AIME 242 (1968), 166-180
15. [CGS] Carr, J., Grustin, M.E., Slemrod, M. Structured phase transitions on a finite interval. Arch. Rat. Mech. Anal. (1986), 317-351
16. ξ - f(u)- CPAM 42 (1989), 523-576
17. [Ch] Chen, Xinfu. Hele-Shaw problem and area preserved curve shortening motion. Arch. Rational Mech. Anal. 123 (1993), 117-151
18. [CP] Constantin, P., Pugh, M. Global solutions for small data to the Hele-Shaw problem. Preprint
19. [DR] Duchon, J., Robert, R. Evolution d'une interface par capillarite et diffusion de volume. I. Existence local en temps. Ann. Inst. Henri Poincaré 1 (1984), 361-378
20. [E] Elliot, C.M. The Cahn-Hilliard model for the kinetics of phase separation. In: Mathematical models for phase change problems. Inst. Sem. of Numerical Math. 88 (Rodrigues, J.F., ed.), Birkhäuser (1989), 35-73
21. [EF] Elliot, C.M., French, D.A. Numerical studies of the Cahn-Hilliard equation for phase separation. IMA Jour. Appl. Math. 38 (1987), 97-128
22. [G1] Grant, G. Spinodal decomposition for the Cahn-Hilliard equation. Preprint
23. [G2] Grant G. Slow motion in one-dimensional Cahn-Morral systems. To appear in SIAM J. Math. Anal., 1994
24. [H] Hale, J.K. Asymptotic behavior of dissipative systems. Mathematical Surveys and Monographs 25, AMS.
25. [He] Henry, D., Geometric Theory of Parabolic Equations, Lecture Notes on Mathematics 840, Springer, 1981
26. [M] Modica, L. The gradient theory of phase transitions and the minimal interface criterion. Arch. Rat. Mech. Anal. 98 (1987), 123-142
27. [N] Neu, J., Unpublished lecture notes
28. [P] Pego, R.L. Front migration in the nonlinear Cahn-Hilliard equation. Proc. Roy. Soc. London A 422 (1989), 261-278
29. [S] Sternberg, P. The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988), 209-260
30. [Si] Simon, L., Asymptotics for a class of non-linear evolution equations, with applications to geometric problems. Ann. of Math. (2) 118 (1983), 517-525
31. [St] Sloth, B. Convergence of the Cahn-Hilliard equation to the Mullins-Sekerka problem in spherical symmetry. Preprint