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On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids
Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint
1. | Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522 |
2. | Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301 |
References:
[1] |
M. Aso, M. Frémond and N. Kenmochi, Parabolic systems with the unknown dependent constraints arising in phase transitions, Internat. Ser. Numer. Math., Birkhäuser Verlag, Basel, 154 (2007), 45-54.
doi: 10.1007/978-3-7643-7719-9_5. |
[2] |
H. Attuoch, Variational Convergence for Functions and Operators, Pitman Advanced Publishing Program, Pitman, Boston, 1984. |
[3] |
A. Azevedo and L. Santos, A diffusion problem with gradient constraint depending on the temperature, Adv. Math. Sci. Appl., 20 (2010), 153-168. |
[4] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans Les Espaces de Hilbert, North-Holland, Amsterdam, 1973. |
[5] |
T. Fukao and N. Kenmochi, Variational inequality for the Navier-Stokes equations with time-dependent constraint, GAKUTO Internat. Ser. Math. Sci. Appl., 34 (2011), 87-102. |
[6] |
T. Fukao and N. Kenmochi, A thermohydraulics model with temperature dependent constraint on velocity fields, Discrete Contin. Dyn. Syst. Ser. S, 7 (2014), 17-34.
doi: 10.3934/dcdss.2014.7.17. |
[7] |
T. Fukao and N. Kenmochi, Parabolic variational inequalities with weakly time-dependent constraints, Adv. Math. Sci. Appl., 23 (2013), 365-395. |
[8] |
A. Kadoya, Y. Murase and N. Kenmochi, A class of nonlinear parabolic systems with environmental constraints, Adv. Math. Sci. Appl., 20 (2010), 281-313. |
[9] |
R. Kano, Y. Murase and N. Kenmochi, Nonlinear evolution equations generated by subdifferentials with nonlocal constraints, Banach Center Publ., 86 (2009), 175-194.
doi: 10.4064/bc86-0-11. |
[10] |
R. Kano, N. Kenmochi and Y. Murase, Parabolic quasi-variational inequalities with non-local constraints, Adv. Math. Sci. Appl., 19 (2009), 565-583. |
[11] |
N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math., 22 (1975), 304-331.
doi: 10.1007/BF02761596. |
[12] |
N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Edu., Chiba Univ., 30 (1981), 1-87. |
[13] |
N. Kenmochi, Monotonicity and compactness methods for nonlinear variational inequalities, Handbook of Differential Equations: Stationary Partial Differential Equations, North-Holland, Amsterdam, 4 (2007), 203-298.
doi: 10.1016/S1874-5733(07)80007-6. |
[14] |
N. Kenmochi, Parabolic quasi-variational diffusion problems with gradient constraints, Discrete Contin. Dyn. Syst. Ser. S., 6 (2013), 423-438.
doi: 10.3934/dcdss.2013.6.423. |
[15] |
J. F. Rodrigues and L. Santos, A parabolic quasi-variational inequality arising in a superconductivity model, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 29 (2000), 153-169. |
[16] |
K. Shirakawa, A. Ito, N. Yamazaki and N. Kenmochi, Asymptotic stability for evolution equations governed by subdifferentials, GAKUTO Internat. Ser. Math. Sci. Appl., 11 (1998), 287-310. |
[17] |
Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 23 (1976), 491-515. |
show all references
References:
[1] |
M. Aso, M. Frémond and N. Kenmochi, Parabolic systems with the unknown dependent constraints arising in phase transitions, Internat. Ser. Numer. Math., Birkhäuser Verlag, Basel, 154 (2007), 45-54.
doi: 10.1007/978-3-7643-7719-9_5. |
[2] |
H. Attuoch, Variational Convergence for Functions and Operators, Pitman Advanced Publishing Program, Pitman, Boston, 1984. |
[3] |
A. Azevedo and L. Santos, A diffusion problem with gradient constraint depending on the temperature, Adv. Math. Sci. Appl., 20 (2010), 153-168. |
[4] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans Les Espaces de Hilbert, North-Holland, Amsterdam, 1973. |
[5] |
T. Fukao and N. Kenmochi, Variational inequality for the Navier-Stokes equations with time-dependent constraint, GAKUTO Internat. Ser. Math. Sci. Appl., 34 (2011), 87-102. |
[6] |
T. Fukao and N. Kenmochi, A thermohydraulics model with temperature dependent constraint on velocity fields, Discrete Contin. Dyn. Syst. Ser. S, 7 (2014), 17-34.
doi: 10.3934/dcdss.2014.7.17. |
[7] |
T. Fukao and N. Kenmochi, Parabolic variational inequalities with weakly time-dependent constraints, Adv. Math. Sci. Appl., 23 (2013), 365-395. |
[8] |
A. Kadoya, Y. Murase and N. Kenmochi, A class of nonlinear parabolic systems with environmental constraints, Adv. Math. Sci. Appl., 20 (2010), 281-313. |
[9] |
R. Kano, Y. Murase and N. Kenmochi, Nonlinear evolution equations generated by subdifferentials with nonlocal constraints, Banach Center Publ., 86 (2009), 175-194.
doi: 10.4064/bc86-0-11. |
[10] |
R. Kano, N. Kenmochi and Y. Murase, Parabolic quasi-variational inequalities with non-local constraints, Adv. Math. Sci. Appl., 19 (2009), 565-583. |
[11] |
N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math., 22 (1975), 304-331.
doi: 10.1007/BF02761596. |
[12] |
N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Edu., Chiba Univ., 30 (1981), 1-87. |
[13] |
N. Kenmochi, Monotonicity and compactness methods for nonlinear variational inequalities, Handbook of Differential Equations: Stationary Partial Differential Equations, North-Holland, Amsterdam, 4 (2007), 203-298.
doi: 10.1016/S1874-5733(07)80007-6. |
[14] |
N. Kenmochi, Parabolic quasi-variational diffusion problems with gradient constraints, Discrete Contin. Dyn. Syst. Ser. S., 6 (2013), 423-438.
doi: 10.3934/dcdss.2013.6.423. |
[15] |
J. F. Rodrigues and L. Santos, A parabolic quasi-variational inequality arising in a superconductivity model, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 29 (2000), 153-169. |
[16] |
K. Shirakawa, A. Ito, N. Yamazaki and N. Kenmochi, Asymptotic stability for evolution equations governed by subdifferentials, GAKUTO Internat. Ser. Math. Sci. Appl., 11 (1998), 287-310. |
[17] |
Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 23 (1976), 491-515. |
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