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A well-posedness result for irreversible phase transitions with a nonlinear heat flux law
An asymptotic analysis for a nonstandard Cahn-Hilliard system with viscosity
1. | Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia |
2. | Dipartimento di Ingegneria Civile, Università di Roma "Tor Vergata", Via del Politecnico 1, 00133 Roma, Italy |
3. | Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany |
References:
[1] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Leyden, 1976.
doi: 10.2165/00003495-197612040-00004. |
[2] |
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167-178. |
[3] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Existence and uniqueness of a global-in-time solution to a phase segregation problem of the Allen-Cahn type, Math. Models Methods Appl. Sci., 20 (2010), 519-541. |
[4] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, A temperature-dependent phase segregation problem of the Allen-Cahn type, Adv. Math. Sci. Appl., 20 (2010), 219-234. |
[5] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system, SIAM J. Appl. Math., 71 (2011), 1849-1870. |
[6] |
E. DiBenedetto, "Degenerate Parabolic Equations," Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-0895-2_6. |
[7] |
M. Frémond, "Non-smooth Thermomechanics," Springer-Verlag, Berlin, 2002. |
[8] |
E. Fried and M. E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Phys. D, 68 (1993), 326-343. |
[9] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192. |
[10] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires," Dunod Gauthier-Villars, Paris, 1969. |
[11] |
P. Podio-Guidugli, Models of phase segregation and diffusion of atomic species on a lattice, Ric. Mat., 55 (2006), 105-118. |
[12] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura. Appl., 146 (1987), 65-96. |
show all references
References:
[1] |
V. Barbu, "Nonlinear Semigroups and Differential Equations in Banach Spaces," Noordhoff, Leyden, 1976.
doi: 10.2165/00003495-197612040-00004. |
[2] |
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13 (1963), 167-178. |
[3] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Existence and uniqueness of a global-in-time solution to a phase segregation problem of the Allen-Cahn type, Math. Models Methods Appl. Sci., 20 (2010), 519-541. |
[4] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, A temperature-dependent phase segregation problem of the Allen-Cahn type, Adv. Math. Sci. Appl., 20 (2010), 219-234. |
[5] |
P. Colli, G. Gilardi, P. Podio-Guidugli and J. Sprekels, Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system, SIAM J. Appl. Math., 71 (2011), 1849-1870. |
[6] |
E. DiBenedetto, "Degenerate Parabolic Equations," Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-0895-2_6. |
[7] |
M. Frémond, "Non-smooth Thermomechanics," Springer-Verlag, Berlin, 2002. |
[8] |
E. Fried and M. E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Phys. D, 68 (1993), 326-343. |
[9] |
M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D, 92 (1996), 178-192. |
[10] |
J. L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires," Dunod Gauthier-Villars, Paris, 1969. |
[11] |
P. Podio-Guidugli, Models of phase segregation and diffusion of atomic species on a lattice, Ric. Mat., 55 (2006), 105-118. |
[12] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura. Appl., 146 (1987), 65-96. |
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