Dynamical Systems for Non-Isothermal Phase Separation

  • Alain Damlamian
  • Nobuyuki Kenmochi
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)


A non-isothermal model for phase separation in a binary mixture is considered. In this paper we try the subdifferential approach to the model, based on the recent development of nonlinear operator -△α defined on the dual space the Sobolev space H 1(Ω).


Phase Field Model Homogeneous Neumann Boundary Condition Phase Transition Model Phase Separation Model Maximal Monotone Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.W. Alt and I. Pawlow, Existence of solutions for non-isothermal phase separation, Adv. Math. Sci. Appl. 1(1992),319–409.MathSciNetzbMATHGoogle Scholar
  2. 2.
    H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Nonlinear Functional Analysis, ed. E. Zarantonello, Academic Press, New York, 1971.Google Scholar
  3. 3.
    H. Brézis, Intégral convexes dans les espaces de Sobolev, Israel J. Math. 13(1972), 9–23.MathSciNetCrossRefGoogle Scholar
  4. 4.
    P. Colli and G. Savaré, Time-discretization of Stefan problems with singular flux, pp. 16–28, in Free Boundary Problems, Theory and Applications, Pitman Research Notes Math. Ser. Vol. 363, Longman, 1996.Google Scholar
  5. 5.
    P._Colli and J. Sprekels, Stefan problems and the Penrose-Fife phase field models, Adv. Math. Sci. Appl., to appear.Google Scholar
  6. 6.
    A._Damlamian, Some results on the multi-phase Stefan problems, Communs. Partial Diff. Eqns. 2(1977), 1017–1044.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    A. Damlamian and N. Kenmochi, Evolution equations generated by subdifferentials in the dual space of H 1(Ω), submitted to Discrete and Continuous Dynamical Systems.Google Scholar
  8. 8.
    A. Damlamian and N. Kenmochi, Evolution equations associated with non-isothermal phase transitions, in Functional Analysis and Global Analysis, Lecture Notes Math., Springer-Verlag, Singapore, to appear.Google Scholar
  9. 9.
    A. Damlamian and N. Kenmochi, Evolution equations associated with non-isothermal phase separation: Subdifferential approach, preprint, 1997.Google Scholar
  10. 10.
    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.MathSciNetADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Alain Damlamian
    • 1
  • Nobuyuki Kenmochi
    • 2
  1. 1.Centre de Mathématiques, Ecole PolytechniqueURA 169 CNRSPalaiseau CedexFrance
  2. 2.Department of Mathematics, Faculty of EducationChiba UniversityInage-ku, ChibaJapan

Personalised recommendations