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On singular Navier-Stokes equations and irreversible phase transitions
1. | Departamento de Matemática, Instituto de Matem, Brazil |
2. | Departamento de Matem, Brazil |
3. | Departamento de Matemática, IMECC - UNICAMP, Rua Sergio Buarque de Holanda, 651, 13083-859 Campinas, SP |
References:
[1] |
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces," 2nd edition, Academic Press, New York, 2003. |
[2] |
M. Aso, M. Frémond and N. Kenmochi, Parabolic systems with the unknown dependent constraints arising in phase transitions, "Free Boundary Problems: Theory and Applications" (eds. I. N. Figueiredo, J. N. Rodrigues and L. Santos),
doi: 10.1007/978-3-7643-7719-9_5. |
[3] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Leyden, 1976. |
[4] |
J. L. Boldrini and G. Planas, A tridimensional phase-field model with convection for phase change of an alloy, Discrete Continuous Dynam. Systems - A, 13 (2005), 429-450.
doi: 10.3934/dcds.2005.13.429. |
[5] |
J. L. Boldrini and G. Planas, Some thoughts on mathematical modeling of solidification and melting, Boletín de la Sociedad Española de Matemática Aplicada, 41 (2007), 77-90. |
[6] |
E. Bonetti, Global solution to a nonlinear phase transition model with dissipation, Adv. Math. Sci. Appl., 12 (2002), 355-376. |
[7] |
G. Bonfanti, M. Frémond and F. Luterotti, Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl., 10 (2000), 1-24. |
[8] |
H. Brezis, "Opératours Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland Math. Studies, 5, North Holland, Amsterdan, 1973. |
[9] |
P. Colli, F. Luterotti, G. Schimperna and U. Stefanelli, Global existence for a class of generalized systems for irreversible phase changes, NoDEA, Nonlinear Differ. Equ. Appl., 9 (2002), 255-276.
doi: 10.1007/s00030-002-8127-8. |
[10] |
K-H. Hoffmann and L. Jiang, Optimal control of a phase field model for solidification, Numer. Funct. Anal. and Optim., 13 (1992), 11-27.
doi: 10.1080/01630569208816458. |
[11] |
P. Laurençot, G. Schimperma and U. Stefanelli, Global existence of a strong solution to the one-dimensional full model for irreversible phase transitions, J. Math. Anal. Appl., 271 (2002), 426-442.
doi: 10.1016/S0022-247X(02)00127-0. |
[12] |
F. Luterotti, G. Schimperma and U. Stefanelli, Global solution to a phase field model with irreversible and constrained phase evolution, Quart. Appl. Math., 60 (2002), 301-316. |
[13] |
G. Planas and J. L. Boldrini, A bidimensional phase-field model with convection for change phase of an alloy, J. Math. Anal. Appl., 303 (2005), 669-687.
doi: 10.1016/j.jmaa.2004.08.068. |
[14] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
show all references
References:
[1] |
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces," 2nd edition, Academic Press, New York, 2003. |
[2] |
M. Aso, M. Frémond and N. Kenmochi, Parabolic systems with the unknown dependent constraints arising in phase transitions, "Free Boundary Problems: Theory and Applications" (eds. I. N. Figueiredo, J. N. Rodrigues and L. Santos),
doi: 10.1007/978-3-7643-7719-9_5. |
[3] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Leyden, 1976. |
[4] |
J. L. Boldrini and G. Planas, A tridimensional phase-field model with convection for phase change of an alloy, Discrete Continuous Dynam. Systems - A, 13 (2005), 429-450.
doi: 10.3934/dcds.2005.13.429. |
[5] |
J. L. Boldrini and G. Planas, Some thoughts on mathematical modeling of solidification and melting, Boletín de la Sociedad Española de Matemática Aplicada, 41 (2007), 77-90. |
[6] |
E. Bonetti, Global solution to a nonlinear phase transition model with dissipation, Adv. Math. Sci. Appl., 12 (2002), 355-376. |
[7] |
G. Bonfanti, M. Frémond and F. Luterotti, Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl., 10 (2000), 1-24. |
[8] |
H. Brezis, "Opératours Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland Math. Studies, 5, North Holland, Amsterdan, 1973. |
[9] |
P. Colli, F. Luterotti, G. Schimperna and U. Stefanelli, Global existence for a class of generalized systems for irreversible phase changes, NoDEA, Nonlinear Differ. Equ. Appl., 9 (2002), 255-276.
doi: 10.1007/s00030-002-8127-8. |
[10] |
K-H. Hoffmann and L. Jiang, Optimal control of a phase field model for solidification, Numer. Funct. Anal. and Optim., 13 (1992), 11-27.
doi: 10.1080/01630569208816458. |
[11] |
P. Laurençot, G. Schimperma and U. Stefanelli, Global existence of a strong solution to the one-dimensional full model for irreversible phase transitions, J. Math. Anal. Appl., 271 (2002), 426-442.
doi: 10.1016/S0022-247X(02)00127-0. |
[12] |
F. Luterotti, G. Schimperma and U. Stefanelli, Global solution to a phase field model with irreversible and constrained phase evolution, Quart. Appl. Math., 60 (2002), 301-316. |
[13] |
G. Planas and J. L. Boldrini, A bidimensional phase-field model with convection for change phase of an alloy, J. Math. Anal. Appl., 303 (2005), 669-687.
doi: 10.1016/j.jmaa.2004.08.068. |
[14] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl., 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
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