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Variational inequalities for a non-isothermal phase field model

Abstract / Introduction Related Papers Cited by
  • We study variational inequalities for a non-isothermal phase field model of the Penrose-Fife type. We consider time-dependent constraints for the order parameter and the Dirichlet boundary condition for the temperature.
    Mathematics Subject Classification: Primary: 35K55, 35K85; Secondary: 82C26.


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  • [1]

    H. Brézis, "Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert," North-Holland, Amsterdam, London, New York, 1973.


    M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions," Appl. Math. Sci., 121, Springer-Verlag, New York, 1996.


    X. Chen and C. M. Elliott, Asymptotics for a parabolic double obstacle problem, Proc. Roy. Soc. London Ser. A, 444 (1994), 429-445.doi: 10.1098/rspa.1994.0030.


    A. Damlamian and N. Kenmochi, Le problème de Stefan avec conditions latérales variables, Hiroshima Math. J., 10 (1980), 271-293.


    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), 370-383.doi: 10.1016/j.nonrwa.2006.11.005.


    N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bull. Fac. Educ. Chiba Univ., 30 (1987), 1-87.


    N. Kenmochi and M. Kubo, Weak solutions of nonlinear systems for non-isothermal phase transitions, Adv. Math. Sci. Appl., 9 (1999), 499-521.


    N. Kenmochi and M. Niezgódka, Evolution systems of nonlinear variational inequalities arising from phase change problems, Nonlinear Anal., 22 (1994), 1163-1180.doi: 10.1016/0362-546X(94)90235-6.


    N. Kenmochi and I. Pawlow, Parabolic-elliptic free boundary problems with time-dependent obstacles, Japan J. Appl. Math., 5 (1988), 87-121.doi: 10.1007/BF03167902.


    M. Kubo, Well-posedness of initial boundary value problem of degenerate parabolic equations, Nonlinear Anal., 63 (2005), e2629-e2637.doi: 10.1016/j.na.2005.03.029.


    M. Kubo and Q. Lu, Evolution equation for nonlinear degenerate parabolic PDE, Nonlinear Anal., 64 (2006), 1849-1859.doi: 10.1016/j.na.2005.07.027.


    K. Kumazaki, A. Ito and M. Kubo, A non-isothermal phase separation with constraints and Dirichlet boundary condition for temperature, Nonlinear Anal., 71 (2009), 1950-1963.doi: 10.1016/j.na.2009.01.039.


    K. Kumazaki, A. Ito and M. Kubo, Generalized solution of a non-isothermal phase separation model, Discrete Contin. Dyn. Syst. 2009, Dynamical Systems and Differential Equations, Proceedings of the 7th AIMS International Conference, suppl., 476-485.


    O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Phys. D, 43 (1990), 44-62.doi: 10.1016/0167-2789(90)90015-H.


    Y. Yamada, On evolution equations generated by subdifferential operators, J. Fac. Sci., Univ. Tokyo, Sect. IA Math., 43 (1976), 491-515.

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