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Phase separation in a gravity field
Variational inequalities for a non-isothermal phase field model
1. | Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555 |
2. | Department of Mathematics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555 |
References:
[1] |
H. Brézis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,", North-Holland, (1973).
|
[2] |
M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,", Appl. Math. Sci., 121 (1996).
|
[3] |
X. Chen and C. M. Elliott, Asymptotics for a parabolic double obstacle problem,, Proc. Roy. Soc. London Ser. A, 444 (1994), 429.
doi: 10.1098/rspa.1994.0030. |
[4] |
A. Damlamian and N. Kenmochi, Le problème de Stefan avec conditions latérales variables,, Hiroshima Math. J., 10 (1980), 271.
|
[5] |
A. Ito and M. Kubo, Well-posedness for an extended Penrose-Fife phase field model with energy balance supplied by Dirichlet boundary conditions,, Nonlinear Anal., 9 (2008), 370.
doi: 10.1016/j.nonrwa.2006.11.005. |
[6] |
N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications,, Bull. Fac. Educ. Chiba Univ., 30 (1987), 1. Google Scholar |
[7] |
N. Kenmochi and M. Kubo, Weak solutions of nonlinear systems for non-isothermal phase transitions,, Adv. Math. Sci. Appl., 9 (1999), 499.
|
[8] |
N. Kenmochi and M. Niezgódka, Evolution systems of nonlinear variational inequalities arising from phase change problems,, Nonlinear Anal., 22 (1994), 1163.
doi: 10.1016/0362-546X(94)90235-6. |
[9] |
N. Kenmochi and I. Pawlow, Parabolic-elliptic free boundary problems with time-dependent obstacles,, Japan J. Appl. Math., 5 (1988), 87.
doi: 10.1007/BF03167902. |
[10] |
M. Kubo, Well-posedness of initial boundary value problem of degenerate parabolic equations,, Nonlinear Anal., 63 (2005).
doi: 10.1016/j.na.2005.03.029. |
[11] |
M. Kubo and Q. Lu, Evolution equation for nonlinear degenerate parabolic PDE,, Nonlinear Anal., 64 (2006), 1849.
doi: 10.1016/j.na.2005.07.027. |
[12] |
K. Kumazaki, A. Ito and M. Kubo, A non-isothermal phase separation with constraints and Dirichlet boundary condition for temperature,, Nonlinear Anal., 71 (2009), 1950.
doi: 10.1016/j.na.2009.01.039. |
[13] |
K. Kumazaki, A. Ito and M. Kubo, Generalized solution of a non-isothermal phase separation model,, Discrete Contin. Dyn. Syst. 2009, 2009 (2009), 476.
|
[14] |
O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions,, Phys. D, 43 (1990), 44.
doi: 10.1016/0167-2789(90)90015-H. |
[15] |
Y. Yamada, On evolution equations generated by subdifferential operators,, J. Fac. Sci., 43 (1976), 491.
|
show all references
References:
[1] |
H. Brézis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert,", North-Holland, (1973).
|
[2] |
M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,", Appl. Math. Sci., 121 (1996).
|
[3] |
X. Chen and C. M. Elliott, Asymptotics for a parabolic double obstacle problem,, Proc. Roy. Soc. London Ser. A, 444 (1994), 429.
doi: 10.1098/rspa.1994.0030. |
[4] |
A. Damlamian and N. Kenmochi, Le problème de Stefan avec conditions latérales variables,, Hiroshima Math. J., 10 (1980), 271.
|
[5] |
A. Ito and M. Kubo, Well-posedness for an extended Penrose-Fife phase field model with energy balance supplied by Dirichlet boundary conditions,, Nonlinear Anal., 9 (2008), 370.
doi: 10.1016/j.nonrwa.2006.11.005. |
[6] |
N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications,, Bull. Fac. Educ. Chiba Univ., 30 (1987), 1. Google Scholar |
[7] |
N. Kenmochi and M. Kubo, Weak solutions of nonlinear systems for non-isothermal phase transitions,, Adv. Math. Sci. Appl., 9 (1999), 499.
|
[8] |
N. Kenmochi and M. Niezgódka, Evolution systems of nonlinear variational inequalities arising from phase change problems,, Nonlinear Anal., 22 (1994), 1163.
doi: 10.1016/0362-546X(94)90235-6. |
[9] |
N. Kenmochi and I. Pawlow, Parabolic-elliptic free boundary problems with time-dependent obstacles,, Japan J. Appl. Math., 5 (1988), 87.
doi: 10.1007/BF03167902. |
[10] |
M. Kubo, Well-posedness of initial boundary value problem of degenerate parabolic equations,, Nonlinear Anal., 63 (2005).
doi: 10.1016/j.na.2005.03.029. |
[11] |
M. Kubo and Q. Lu, Evolution equation for nonlinear degenerate parabolic PDE,, Nonlinear Anal., 64 (2006), 1849.
doi: 10.1016/j.na.2005.07.027. |
[12] |
K. Kumazaki, A. Ito and M. Kubo, A non-isothermal phase separation with constraints and Dirichlet boundary condition for temperature,, Nonlinear Anal., 71 (2009), 1950.
doi: 10.1016/j.na.2009.01.039. |
[13] |
K. Kumazaki, A. Ito and M. Kubo, Generalized solution of a non-isothermal phase separation model,, Discrete Contin. Dyn. Syst. 2009, 2009 (2009), 476.
|
[14] |
O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions,, Phys. D, 43 (1990), 44.
doi: 10.1016/0167-2789(90)90015-H. |
[15] |
Y. Yamada, On evolution equations generated by subdifferential operators,, J. Fac. Sci., 43 (1976), 491.
|
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