Asymptotic behaviour of solutions to non-isothermal phase separation model with constraint in one-dimensional space

Akio ITO; Nobuyuki KENMOCHI

doi:10.2969/jmsj/05020491

Akio ITO, Nobuyuki KENMOCHI

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ジャーナルフリー

1998 年 50 巻 2 号 p. 491-519

DOI https://doi.org/10.2969/jmsj/05020491

詳細

Published: 1998 Received: 1994/04/27 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Departmant of Mathematics Graduate School of Science and Technology Chiba University
2) Departmant of Mathematics Faculty of Education Chiba University

訂正後 :
1) Department of Mathematics Graduate School of Science and Technology Chiba University
2) Department of Mathematics Faculty of Education Chiba University

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) H.W. Alt and I. Pawlow, Existence of solutions for non-isothermal phase separation, Adv. Math. Sci.Appl. 1 (1992), 319-409.
2) J.F. Blowey and C.M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, Part I: Mathematical analysis, European J. Appl. Math. 2 (1991), 233-280.
3) J.F. Blowey and C.M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, pp. 19-60, in Degenerate Diffusion, IMA 47, Springer-Verlag, New York, 1993.
4) J.F. Blowey and C.M. Elliott, A phase field model with a double obstacle potential, pp. 1-22, in Motion by Mean Curvature, Walter de Gruyter, Berlin-New York, 1994.
5) J. Carr, M.E. Gurtin and M. Slemrod, Structured phase transitions on a finite interval, Arch. Rat. Mech. Anal. 12 (1984), 317-351.
6) N. Chafee and E.F. Infante, A bifurcation problem for a nonlinear partial differential equation of parabolic type, Applicable Anal. 4 (1974), 17-37.
7) X. Chen and C.M. Elliott, Asymptotics for a parabolic double obstacle problem, Royal Soc. London, Proc. Math. Phys. Sci. Ser. A444 (1994), 429-445.
8) C.M. Elliott and S. Zheng, On the Cahn-Hilliard equation, Arch. Rat. Mech. Anal. 96 (1986), 339-357.
9) N. Kenmochi and M. Niezgódka, Nonlinear system for non-isothermal diffusive phase separation, J. Math. Anal. Appl. 188 (1994), 651-679.
10) N. Kenmochi and M. Niezgódka, Large time behaviour of a nonlinear system for phase separation, pp. 12-22, in “Progress in partial differential equations: the Metz surveys 2”. Pitman Research Notes Math. Ser. vol. 290, 1993.
11) N. Kenmochi and M. Niezgódka, Viscosity approach to modelling non-isothermal diffusive phase separations, Japan J. Indust. Appl. Math. 13 (1996), 135-169.
12) N. Kenmochi, M. Niezgódka and I. Pawlow, Subdifferential operator approach to the Cahn-Hilliard equation with constraint, J. Differential Equations 117 (1995), 320-356.
13) O. Penrose and P.C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D, 43 (1990), 44-62.
14) W. Shen and S. Zheng, On the coupled Cahn-Hilliard equations, Commun. in P.D.E., 18 (1993), 711-727.
15) R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, Berlin, 1988.
16) W. von Wahl, On the Cahn-Hilliard equation u'+Δ²u-Δf(u)=0, Delft Progress Report 10 (1985), 291-310.
17) S. Zheng, Asymptotic behaviour of the solution to the Cahn-Hilliard equation, Applicable Anal. 23 (1986), 165-184.

Right : [1] H. W. Alt and I. Pawlow, Existence of solutions for non-isothermal phase separation, Adv. Math. Sci. Appl. 1 (1992), 319-409.
[2] J. F. Blowey and C. M. Elliott, The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy, Part I: Mathematical analysis, European J. Appl. Math. 2 (1991), 233-280.
[3] J. F. Blowey and C. M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, pp. 19-60, in Degenerate Diffusion, IMA 47, Springer-Verlag, New York, 1993.
[4] J. F. Blowey and C. M. Elliott, A phase field model with a double obstacle potential, pp. 1-22, in Motion by Mean Curvature, Walter de Gruyter, Berlin-New York, 1994.
[5] J. Carr, M. E. Gurtin and M. Slemrod, Structured phase transitions on a finite interval, Arch. Rat. Mech. Anal. 12 (1984), 317-351.
[6] N. Chafee and E. F. Infante, A bifurcation problem for a nonlinear partial differential equation of parabolic type, Applicable Anal. 4 (1974), 17-37.
[7] X. Chen and C. M. Elliott, Asymptotics for a parabolic double obstacle problem, Royal Soc. London, Proc. Math. Phys. Sci. Ser. A444 (1994), 429-445.
[8] C. M. Elliott and S. Zheng, On the Cahn-Hilliard equation, Arch. Rat. Mech. Anal. 96 (1986), 339-357.
[9] N. Kenmochi and M. Niezgódka, Nonlinear system for non-isothermal diffusive phase separation, J. Math. Anal. Appl. 188 (1994), 651-679.
[10] N. Kenmochi and M. Niezgódka, Large time behaviour of a nonlinear system for phase separation, pp. 12-22, in “Progress in partial differential equations: the Metz surveys 2”. Pitman Research Notes Math. Ser. vol. 290, 1993.
[11] N. Kenmochi and M. Niezgódka, Viscosity approach to modelling non-isothermal diffusive phase separations, Japan J. Indust. Appl. Math. 13 (1996), 135-169.
[12] N. Kenmochi, M. Niezgódka and I. Pawlow, Subdifferential operator approach to the Cahn-Hilliard equation with constraint, J. Differential Equations 117 (1995), 320-356.
[13] O. Penrose and P. C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D, 43 (1990), 44-62.
[14] W. Shen and S. Zheng, On the coupled Cahn-Hilliard equations, Commun. in P. D. E., 18 (1993), 711-727.
[15] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, Berlin, 1988.
[16] W. von Wahl, On the Cahn-Hilliard equation u'+Δ²u-Δf(u)=0, Delft Progress Report 10 (1985), 291-310.
[17] S. Zheng, Asymptotic behaviour of the solution to the Cahn-Hilliard equation, Applicable Anal. 23 (1986), 165-184.

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