A singular limit for a system of degenerate Cahn-Hilliard equations

Advances in Differential Equations

Volumn 5, Issue 4-6, 2000, Pages 401-434

  Garcke, Harald ^a   Novick Cohen, Amy ^b  

^a UNIVERSITY OF BONN   (Germany)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001019294     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. N. Alikakos, P. Bates, and X. Chen, Convergence of the Cahn-Hilliard equation to the Hele-Shaw model, Arch. Rat. Mech. Anal., 128 (1994), 165-205.
2. S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids, Ann. I. H.P. analyse nonlińeaire, 7 (1990), 37-65.
3. J.W. Barrett and J.F. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Math. Comp., (to appear).
4. J.W. Barrett and J.F. Blowey, Finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix, IMA J. Numerical Analysis, 18 (1998), 287-328.
5. J.F. Blowey, M.I.M. Copetti, and C.M. Elliott, Numerical analysis of a model for phase separation of a multi-component alloy, IMA J. Numerical Analysis, 16 (1995), 111-139.
6. L. Bronsard, H. Garcke, and B. Stoth, A multi-phase Mullins-Sekerka system: matched asymptotic expansions and an implicit time discretization for the geometric evolution problem, Proc. Roy. Soc. Edinburgh, 128 A (1998), 481-506.
7. L. Bronsard, G. Gui, and M. Schatzman, A three layered minimizer in R2 for a variational problem with a symmetric three-well potential, Comm. in Pure and Appl. Math., 47 (1996), 677-715.
8. L. Bronsard and F. Reitich, On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation, Arch. Rat. Mech. Anal., 124 (1993), 355-379.
9. G. Caginalp and P.C. Fife, Dynamics of layered interfaces arising from phase boundaries, SIAM J. Appl. Math., 48 (1988), 506-518.
10. J.W. Cahn, C.M. Elliott, and A. Novick-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature, European J. Appl. Math., 7 (1996), No.3, 287-301.
11. J. W. Cahn and J.E. Hilliard, Spinodal decomposition: A reprise, Acta Metallurgica, Vol. 19 (1971), 151-161.
12. J.W. Cahn and A. Novick-Cohen, Limiting motion for an Allen-Cahn/Cahn-Hilliard system, Proc. of FBP'95, Zakopane, Poland, in "Free Boundary Problems and Applications", ed. M. Niezgodka and P. Strzelecki, (1996), Addison Wesley Longman.
13. X. Chen, J. Hong and F. Yi, Existence, uniqueness and regularity of classical solutions of the Mullins-Sekerka problem, Commun. Partial Diff. Eqns., 21 (1996), 1705-1727.
14. D. De Fontaine, An analysis of clustering and ordering in multicomponent solid solutions-I. stability criteria, Journal Phys. Chem. Solids, 33 (1972), 287-310.
15. P. G. de Gennes, Wetting: statics and dynamics, Rev. of Mod. Phys. 57 No. 3 (1985), 827-863.
16. C.M. Elliott and H. Garcke, On the Cahn-Hilliard equation with degenerate mobility, SIAM Journal on Mathematical Analysis, 27 (1996), Vol. 2, 404-423.
17. C.M. Elliott and H. Garcke, Existence results for diffusive surface motion laws, Adv. in Math. Sciences and Applications, 7 No.1 (1997), 465-488.ü
18. C.M. Elliott and H. Garcke, Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix, Physica D, Vol. 109 (1997), 242 -256.
19. C.M. Elliott and S. Luckhaus, A generalized diffusion equation for phase separation of a multi-component mixture with interfacial free energy, SFB256 University Bonn, Preprint 195 (1991).
20. J. Escher, U.F. Mayer, and G. Simonett, The surface diffusion flow for immersed hypersurfaces, SIAM Journal on Mathematical Analysis, 29 (1998), 1419-1433.
21. J. Escher and G. Simonett, Classical solutions for Hele-Shaw models with surface tension, Adv. Diff. Equ., 2 No. 4 (1997), 619-642.
22. D.J. Eyre, Systems of Cahn-Hilliard equations, SIAM J. Appl. Math., 53 No. 6 (1993), 1686-1712.
23. M.E. Gurtin, Thermodynamics of Evolving Phase Boundaries in the Plane, Clarendon Press (1993), Oxford.
24. J.E. Hilliard, Spinodal decomposition, in Phase Transformations, American Society for Metals, Cleveland, (1970), 497-560.
25. J.E. Morral and J.W. Cahn, Spinodal decomposition in ternary alloys, Acta Metallurgica, 19 (1971), 1037-1045.
26. A. Novick-Cohen, Triple junction motion for Allen-Cahn/Cahn-Hilliard systems, Physica D, to appear.
27. R. Pego, Front migration in the nonlinear Cahn-Hilliard equation, Proc. Roy. Soc. London A, 422 (1989), 261-278.
28. J. Rubinstein, P. Sternberg, and J.B. Keller., Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math., 49 (1989), 116-133.
29. V.A. Solonnikov, Boundary value problems in physics, Proceedings of the Steklov Institute of Mathematics, Vol. LXXXIII (1965).
30. P. Sternberg, Vector-valued local minimizers of nonconvex variational problems, Rocky Mt. J. Math., 21 (2) (1991), 799-807.
31. B. Stoth, Convergence of the Cahn-Hilliard equation to the Mullins-Sekerka problem in spherical symmetry, J. Diff. Equ., 125 Vol. 1 (1996), 154-183.
32. M. Tombakoglu and A. Ziya Akcasu, Dynamics of copolymer and homopolymer mixtures in bulk and in solution via the random phase approximation, Macromolecules, 23 (1990), 607-612.
33. A.A. Wheeler, M.B. McFadden, and W.J. Boettinger, Phase-field model for solidification of a eutectic alloy, Proc. Roy. Soc. Lond. A, 452 (1996), 495-525.
34. T. Young, An essay on the cohesion of fluids, Philos. Trans. Roy. Soc. London, 95 (1805), 65-87.