Surfactants in foam stability: A phase-field model

Archive for Rational Mechanics and Analysis

Volumn 183, Issue 3, 2007, Pages 411-456

  Fonseca, Irene ^a   Morini, Massimiliano ^b   Slastikov, Valeriy ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b SISSA   (Italy)

^c UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846799148     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-006-0012-x     Document Type: Article

References (26)

1. AMBROSIO, L., FUSCO, N., PALLARA, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, New York, 2000
2. AMBROSIO, L., DE LELLIS, C., MANTEGAZZA, C.: Line energies for gradient vector fields in the plane. Calc. Var. Partial Differential Equations 9, 327-355 (1999)
3. AVILES, P., GIGA, Y.: On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg-Landau type energy for gradient fields. Proc. Roy. Soc. Edinburgh Sect. A 129, 1-17 (1999)
4. BALDO, S.: Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 7, 67-90 (1990)
5. BARROSO, A.C., FONSECA, I.: Anisotropic singular perturbations-the vectorial case. Proc. Roy. Soc. Edinburgh Sect. A 124, 527-571 (1994)
6. BOUCHITTÈ, G.: Singular perturbations of variational problems arising from a two-phase transition model. Appl. Math. Optim. 21, 289-314 (1990)
7. BRONSARD, L., KOHN, R.V.: On the slowness of phase boundary motion in one space dimension. Commun. Pure Appl. Math. 43, 983-997 (1990)
8. xx - f(u). Commun. Pure Appl. Math. 42, 523-576 (1989)
9. CONTI, S., FONSECA, I., LEONI, G.: A Γ-convergence result for the two-gradient theory of phase transitions. Commun. Pure Appl. Math. 55, 857-936 (2002)
10. CONTI, S., SCHWEIZER, B.: A sharp-interface limit for the geometrically linear two-well problem in two dimensions. Arch. Ration. Mech. Anal. 179, 413-452 (2006)
11. DAL MASO, G.: An Introduction to Γ-Convergence. Progress in Nonlinear Differential Equations and their Applications, 8. Birkhäuser Boston, 1993
12. FONSECA, I., MANTEGAZZA, C.: Second order singular perturbation models for phase transitions. SIAM J. Math. Anal. 31, 1121-1143 (2000)
13. FONSECA, I., TARTAR, L.: The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinburgh Sect. A 111, 89-102 (1989)
14. GRANT, C.P.: Slow motion in one-dimensional Cahn-Morral systems. SIAM J. Math. Anal. 26, 21-34 (1995)
15. GURTIN, M.E.: Some results and conjectures in the gradient theory of phase transitions. Metastability and Incompletely Posed Problems. IMA Volumes in Mathematics and Its Applications, 3, pp. 135-146. Springer, New York, 1987
16. GURTIN, M.E., MATANO, H.: On the structure of equilibrium phase transitions within the gradient theory of fluids. Quart. Appl. Math. 46, 301-317 (1988)
17. JIN, W., KOHN, R.V.: Singular perturbation and the energy of folds. J. Nonlinear Sci. 10, 355-390 (2000)
18. KRAYNIK, A.M.: Foam structure: From soap froth to solid foams. MRS Bulletin 28, 275-278 (2003)
19. KOHN, R.V., STERNBERG, P.: Local minimisers and singular perturbations. Proc. Roy. Soc. Edinburgh Sect. A 111, 69-84 (1989)
20. --convergenza. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 14, 285-299 (1977)
21. MODICA, L.: The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 98, 123-142 (1987)
22. OWEN, N.C., STERNBERG, P.: Nonconvex variational problems with anisotropic perturbations. Nonlinear Anal. 16, 705-719 (1991)
23. PERKINS, R., SEKERKA, R., WARREN, J., LANGER, S.: Private communication
24. ROCKAFELLAR, R.T.: Convex Analysis. Princeton Mathematical Series, no. 28, Princeton University Press, Princeton, 1970
25. STERNBERG. P.: The effect of a singular perturbation on nonconvex variational problems. Arch. Ration. Mech. Anal. 101, 209-260 (1988)
26. STERNBERG, P.: Vector-valued local minimizers of nonconvex variational problems. Current directions in nonlinear partial differential equations. Rocky Mountain J. Math. 21, 799-807