[2] Adams, R. A.:
Sobolev Spaces. Pure and Applied Mathematics 65. A Series of Monographs and Textbooks Academic Press, New York (1975).
MR 0450957 |
Zbl 0314.46030
[3] Brokate, M., Kenmochi, N., Müller, I., Rodriguez, J. F., Verdi, C.:
Phase transitions and hysteresis. Lectures Given at the Third C.I.M.E., 1993, Montecatini Terme, Italy Lecture Notes in Mathematics 1584 Springer, Berlin (1994), A. Visintin.
MR 1321829
[5] Cahn, J. W., Elliott, C. M., Novick-Cohen, A.:
The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature. Eur. J. Appl. Math. 7 287-301 (1996).
DOI 10.1017/S0956792500002369 |
MR 1401172 |
Zbl 0861.35039
[6] Changchun, L.:
Cahn-Hilliard equation with terms of lower order and non-constant mobility. Electron. J. Qual. Theory Differ. Equ. 2003 (2003), 9 pp. (electronic only).
MR 1986908 |
Zbl 1032.35076
[7] Passo, R. Dal, Giacomelli, L., Novick-Cohen, A.:
Existence for an Allen-Cahn/Cahn-Hilliard system with degenerate mobility. Interfaces Free Bound. 1 199-226 (1999).
DOI 10.4171/IFB/9 |
MR 1867131
[9] Dellacherie, C., Meyer, P.-A.:
Probabilities and Potential. North-Holland Mathematics Studies 29 North-Holland Publishing Company, Amsterdam (1978).
MR 0521810 |
Zbl 0494.60001
[12] Gal, C. G.:
Global well-posedness for the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions. Adv. Differ. Equ. 12 1241-1274 (2007).
MR 2372239 |
Zbl 1162.35386
[15] Heida, M.: Modeling Multiphase Flow in Porous Media with an Application to Permafrost Soil. Univ. Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät, Heidelberg; Charles Univ. Praha, Faculty of Mathematics and Physics (PhD Thesis), Praha (2011).
[16] Heida, M.:
On the derivation of thermodynamically consistent boundary conditions for the Cahn-Hilliard-Navier-Stokes system. Internat. J. Engrg. Sci. 62 126-156 (2013).
DOI 10.1016/j.ijengsci.2012.09.005 |
MR 2996309
[17] Heida, M.:
On systems of Cahn-Hilliard and Allen-Cahn equations considered as gradient flows in Hilbert spaces. J. Math. Anal. Appl. 423 410-455 (2015).
DOI 10.1016/j.jmaa.2014.09.046 |
MR 3273188
[18] Ito, A., Kenmochi, N., Niezgódka, M.:
Large-time behaviour of non-isothermal models for phase separation. Proc. Conf. Elliptic and Parabolic Problems, 1994 Pitman Res. Notes Math. Ser. 325 Longman Scientific & Technical, Harlow 120-151 (1995).
MR 1416579 |
Zbl 0838.35053
[22] Lowengrub, J. S., Rätz, A., Voigt, A.:
Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission. Phys. Rev. E 79 (2009), 031926, 13 pp.
DOI 10.1103/PhysRevE.79.031926 |
MR 2497179
[23] Mercker, M.:
Models, numerics and simulations of deforming biological surfaces. Univ. Heidelberg, Naturwissenschaftlich-Mathematische Gesamtfakultät (PhD Thesis), Heidelberg (2012).
Zbl 1304.92023
[24] Mercker, M., Marciniak-Czochra, A., Richter, T., Hartmann, D.:
Modeling and computing of deformation dynamics of inhomogeneous biological surfaces. SIAM J. Appl. Math. 73 1768-1792 (2013).
DOI 10.1137/120885553 |
MR 3095724 |
Zbl 1282.74015
[25] Mercker, M., Richter, T., Hartmann, D.:
Sorting mechanisms and communication in phase separating coupled monolayers. J. Phys. Chem. B 115 11739-11745, DOI: 10.1021/jp204127g (2011).
DOI 10.1021/jp204127g
[26] Miranville, A.:
Existence of solutions for Cahn-Hilliard type equations. Discrete Contin. Dyn. Syst. 2003 Suppl. Vol., 630-637 (2003).
MR 2018168 |
Zbl 1070.35002
[31] Novick-Cohen, A.:
The Cahn-Hilliard equation. Handbook of Differential Equations: Evolutionary Equations. Vol. IV Elsevier/North-Holland, Amsterdam 201-228 (2008).
MR 2508166 |
Zbl 1185.35001
[32] Novick-Cohen, A.:
The Cahn-Hilliard Equation: From Backwards Diffusion to Surface Diffusion. (to appear) in Cambridge University Press.
MR 2508166
[34] Racke, R., Zheng, S.:
The Cahn-Hilliard equation with dynamic boundary conditions. Adv. Differ. Equ. 8 83-110 (2003).
MR 1946559 |
Zbl 1035.35050
[39] Serfaty, S.:
Gamma-convergence of gradient flows on Hilbert and metric spaces and applications. Discrete Contin. Dyn. Syst. 31 1427-1451 (2011).
MR 2836361 |
Zbl 1239.35015
[42] Temam, R.:
Navier-Stokes Equations. Theory and Numerical Analysis. American Mathematical Society, Providence (2001).
MR 1846644 |
Zbl 0981.35001
[44] Torabi, S., Wise, S., Lowengrub, J., Rätz, A., Voigt, A.: A new method for simulating strongly anisotropic Cahn-Hilliard equations. Materials Science and Technology-Association for Iron and Steel Technology 3 1432-1444 (2007).