Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids

Sisto Baldo

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 2, page 67-90
  • ISSN: 0294-1449

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Baldo, Sisto. "Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids." Annales de l'I.H.P. Analyse non linéaire 7.2 (1990): 67-90. <http://eudml.org/doc/78216>.

@article{Baldo1990,
author = {Baldo, Sisto},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Van der Waals-Cahn-Hilliard theory; phase transitions},
language = {eng},
number = {2},
pages = {67-90},
publisher = {Gauthier-Villars},
title = {Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids},
url = {http://eudml.org/doc/78216},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Baldo, Sisto
TI - Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 2
SP - 67
EP - 90
LA - eng
KW - Van der Waals-Cahn-Hilliard theory; phase transitions
UR - http://eudml.org/doc/78216
ER -

References

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  1. [A] L. Ambrosio (to appear). 
  2. [CH] J.W. Cahn and J.E. Hilliard, Free Energy of a Nonuniform System: I. Interfacial Energy, J. Chem. Ph., Vol. 28, 1958, pp. 258-267. 
  3. [DGF] E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Mat. Fis. Natur., Vol. 58, 1975, pp. 842-850. Zbl0339.49005MR448194
  4. [F] H. Federer, Geometric Measure Theory, Springer Verlag, Berlin1968. Zbl0176.00801MR257325
  5. [FT] I. Fonseca and L. Tartar, The Gradient Theory of Phase Transitions for Systems with two Potential Wells, Preprint Carnegic-Mellon Univ., Pittsburgh, 1988. MR985992
  6. [Gi] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhauser Verlag, 1984. Zbl0545.49018MR775682
  7. [GM] M.E. Gurtin and H. Matano, On the Structure of Equilibrium Phase Transitions within the Gradient Theory of Fluids, Quarterly of Appl. Math., Vol. 46, 1988. Zbl0665.76120MR950604
  8. [LM] S. Luckaus and L. Modica, The Gibbs-Thompson Relation within the Gradient Theory of Phase Transitions (to appear). 
  9. [M1] L. Modica, The Gradient Theory of Phase Transitions and the Minimal Interface Criterion, Arch. Rat. Mech. & Analysis, 98, 1987, pp. 123-142. Zbl0616.76004
  10. [M2] L. Modica, Gradient Theory of Phase Transitions with Boundary Contact Energy, Ann. Inst. H. Poincaré. Anal. nonlin., Vol. 4, 1987, pp.487-512. Zbl0642.49009MR921549
  11. [QG] T.Q. De Gromard, Approximation forte dans BV(Ω), C. R. Acad. Sci. Paris, T. 301, 1985, pp. 261-264. Zbl0593.46026MR803213
  12. [S] P. Sternberg, The Effect of a Singular Perturbation on Nonconvex Variational Problems, Arch. Rat. Mech. & Analysis, Vol. 101, 1988, pp. 209-260. Zbl0647.49021
  13. [Vo] A.I. Vol'pert, The Spaces BV and Quasilinear Equations, Mat. Sbornik., Vol. 73, 1967, pp. 225-254. Zbl0168.07402MR216338
  14. [VW] J.D. Van Der Waals, The Thermodynamic Theory of Capillarity under the Hypothesis of a Continuous Variation of Density, Verhaendel. Kronik. Akad. Weten. Amsterdam, Vol. 1, 1893. 

Citations in EuDML Documents

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  1. Giovanni Leoni, A remark on the compactness for the Cahn–Hilliard functional
  2. Blaise Bourdin, Antonin Chambolle, Design-dependent loads in topology optimization
  3. Luigi Ambrosio, Metric space valued functions of bounded variation
  4. Gian Paolo Leonardi, Γ -convergence of constrained Dirichlet functionals
  5. Blaise Bourdin, Antonin Chambolle, Design-dependent loads in topology optimization
  6. Luise Blank, Harald Garcke, M. Hassan Farshbaf-Shaker, Vanessa Styles, Relating phase field and sharp interface approaches to structural topology optimization

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