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On the higher-dimensional multifractal analysis
On a phase field model for solid-liquid phase transitions
1. | Université de Lyon, CNRS UMR 5208 & Université Lyon 1, Institut Camille Jordan, 43 bd du 11 novembre 1918, F-69622 Villeurbanne cedex, France, France |
2. | Université Blaise Pascal & CNRS UMR 6620, Laboratoire de Mathématiques, Campus des Cézeaux, B.P. 80026, F-63177 Aubière cedex, France |
3. | CEA-Grenoble (DEN/DTP/SMTH), 17, rue des martyrs, F-38054 Grenoble cedex 9, France |
References:
[1] |
D. M. Anderson, G. B. McFadden and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, in "Annual Review of Fluid Mechanics," Vol. 30, Annual Reviews, Palo Alto, CA, (1998), 139-165. |
[2] |
E. Bonetti, P. Colli, M. Fabrizio and G. Gilardi, Existence and boundedness of solutions for a singular phase field system, J. Differential Equations, 246 (2009), 3260-3295. |
[3] |
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.
doi: 10.1007/BF00254827. |
[4] |
G. Caginalp and X. Chen, Convergence of the phase field model to its sharp interface limits, European J. Appl. Math., 9 (1998), 417-445.
doi: 10.1017/S0956792598003520. |
[5] |
C. Cavaterra, C. G. Gal, M. Grasselli and A. Miranville, Phase-field systems with nonlinear coupling and dynamic boundary conditions, Nonlinear Anal., 72 (2010), 2375-2399.
doi: 10.1016/j.na.2009.11.002. |
[6] |
P. Colli, D. Hilhorst, F. Issard-Roch and G. Schimperna, Long time convergence for a class of variational phase-field models, Discrete Contin. Dyn. Syst., 25 (2009), 63-81. |
[7] |
E. Feireisl, H. Petzeltová and E. Rocca, Existence of solutions to a phase transition model with microscopic movements, Math. Methods Appl. Sci., 32 (2009), 1345-1369. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001. |
[9] |
M. Grasselli, A. Miranville and G. Schimperna, The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials, Discrete Contin. Dyn. Syst., 28 (2010), 67-98. |
[10] |
M. Grasselli, H. Petzeltová and G. Schimperna, Long time behavior of solutions to the Caginalp system with singular potential, Z. Anal. Anwend., 25 (2006), 51-72.
doi: 10.4171/ZAA/1277. |
[11] |
A. Miranville and R. Quintanilla, A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear Anal., 71 (2009), 2278-2290.
doi: 10.1016/j.na.2009.01.061. |
[12] |
A. Miranville and R. Quintanilla, A Caginalp phase-field system with a nonlinear coupling, Nonlinear Anal. Real World Appl., 11 (2010), 2849-2861.
doi: 10.1016/j.nonrwa.2009.10.008. |
[13] |
Pierre Ruyer, "Modèle de Champ de Phase pour l'Étude de l'Ébullition," Ph.D thesis, École Polytechnique, 2006. |
show all references
References:
[1] |
D. M. Anderson, G. B. McFadden and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, in "Annual Review of Fluid Mechanics," Vol. 30, Annual Reviews, Palo Alto, CA, (1998), 139-165. |
[2] |
E. Bonetti, P. Colli, M. Fabrizio and G. Gilardi, Existence and boundedness of solutions for a singular phase field system, J. Differential Equations, 246 (2009), 3260-3295. |
[3] |
G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.
doi: 10.1007/BF00254827. |
[4] |
G. Caginalp and X. Chen, Convergence of the phase field model to its sharp interface limits, European J. Appl. Math., 9 (1998), 417-445.
doi: 10.1017/S0956792598003520. |
[5] |
C. Cavaterra, C. G. Gal, M. Grasselli and A. Miranville, Phase-field systems with nonlinear coupling and dynamic boundary conditions, Nonlinear Anal., 72 (2010), 2375-2399.
doi: 10.1016/j.na.2009.11.002. |
[6] |
P. Colli, D. Hilhorst, F. Issard-Roch and G. Schimperna, Long time convergence for a class of variational phase-field models, Discrete Contin. Dyn. Syst., 25 (2009), 63-81. |
[7] |
E. Feireisl, H. Petzeltová and E. Rocca, Existence of solutions to a phase transition model with microscopic movements, Math. Methods Appl. Sci., 32 (2009), 1345-1369. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001. |
[9] |
M. Grasselli, A. Miranville and G. Schimperna, The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials, Discrete Contin. Dyn. Syst., 28 (2010), 67-98. |
[10] |
M. Grasselli, H. Petzeltová and G. Schimperna, Long time behavior of solutions to the Caginalp system with singular potential, Z. Anal. Anwend., 25 (2006), 51-72.
doi: 10.4171/ZAA/1277. |
[11] |
A. Miranville and R. Quintanilla, A generalization of the Caginalp phase-field system based on the Cattaneo law, Nonlinear Anal., 71 (2009), 2278-2290.
doi: 10.1016/j.na.2009.01.061. |
[12] |
A. Miranville and R. Quintanilla, A Caginalp phase-field system with a nonlinear coupling, Nonlinear Anal. Real World Appl., 11 (2010), 2849-2861.
doi: 10.1016/j.nonrwa.2009.10.008. |
[13] |
Pierre Ruyer, "Modèle de Champ de Phase pour l'Étude de l'Ébullition," Ph.D thesis, École Polytechnique, 2006. |
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