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Phase transitions of a phase field model
1. | Department of Mathematics, Indiana University, Bloomington, IN 47405, United States |
References:
[1] |
J. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[2] |
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in "Mathematical Models for Phase Change Problems (Internat. Ser. Numer. Math. 88)" (eds. J. F. Rodriques), Birkhäuser-Verlag, Basel, Switzerland, (1989), 35-73. |
[3] |
M. E. Gurtin, D. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci., 6 (1996), 815-831.
doi: 10.1142/S0218202596000341. |
[4] |
P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys., 49 (1977), 435-479.
doi: 10.1103/RevModPhys.49.435. |
[5] |
C. Hsia, Bifurcation of binary systems with the Onsager mobility, J. Math. Phys., 51 (2010), 063305.
doi: 10.1063/1.3406383. |
[6] |
C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method, Physica D, 179 (2003), 211-228.
doi: 10.1016/S0167-2789(03)00030-7. |
[7] |
T. Ma and S. Wang, "Phase Transition Dynamics in Nonlinear Sciences," to appear. |
[8] |
T. Ma and S. Wang, "Bifurcation Theory and Applications," vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. |
[9] |
T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamics for binary systems, Disc. Cont. Dyn. Sys. B, 11 (2009), 741-784.
doi: 10.3934/dcdsb.2009.11.741. |
[10] |
T. Ma and S. Wang, Phase separation of binary systems, Physica A, 388 (2009), 4811-4817.
doi: 10.1016/j.physa.2009.07.044. |
[11] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation, Asymptotic Anal., 22 (2000), 235-259. |
[12] |
A. Novich-Cohen and L. A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D, 10 (1984), 277-298.
doi: 10.1016/0167-2789(84)90180-5. |
[13] |
X. P. Wang and Y. G. Wang, The sharp interface limit of a phase field model for moving contact line problem, Methods Appl. Anal., 14 (2007), 287-284. |
show all references
References:
[1] |
J. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267.
doi: 10.1063/1.1744102. |
[2] |
C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in "Mathematical Models for Phase Change Problems (Internat. Ser. Numer. Math. 88)" (eds. J. F. Rodriques), Birkhäuser-Verlag, Basel, Switzerland, (1989), 35-73. |
[3] |
M. E. Gurtin, D. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci., 6 (1996), 815-831.
doi: 10.1142/S0218202596000341. |
[4] |
P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys., 49 (1977), 435-479.
doi: 10.1103/RevModPhys.49.435. |
[5] |
C. Hsia, Bifurcation of binary systems with the Onsager mobility, J. Math. Phys., 51 (2010), 063305.
doi: 10.1063/1.3406383. |
[6] |
C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method, Physica D, 179 (2003), 211-228.
doi: 10.1016/S0167-2789(03)00030-7. |
[7] |
T. Ma and S. Wang, "Phase Transition Dynamics in Nonlinear Sciences," to appear. |
[8] |
T. Ma and S. Wang, "Bifurcation Theory and Applications," vol. 53 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. |
[9] |
T. Ma and S. Wang, Cahn-Hilliard equations and phase transition dynamics for binary systems, Disc. Cont. Dyn. Sys. B, 11 (2009), 741-784.
doi: 10.3934/dcdsb.2009.11.741. |
[10] |
T. Ma and S. Wang, Phase separation of binary systems, Physica A, 388 (2009), 4811-4817.
doi: 10.1016/j.physa.2009.07.044. |
[11] |
A. Miranville, Some generalizations of the Cahn-Hilliard equation, Asymptotic Anal., 22 (2000), 235-259. |
[12] |
A. Novich-Cohen and L. A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D, 10 (1984), 277-298.
doi: 10.1016/0167-2789(84)90180-5. |
[13] |
X. P. Wang and Y. G. Wang, The sharp interface limit of a phase field model for moving contact line problem, Methods Appl. Anal., 14 (2007), 287-284. |
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