On the singular limit in a phase field model of phase transitions

Nicholas D. Alikakos; Peter W. Bates

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 2, page 141-178
  • ISSN: 0294-1449

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Alikakos, Nicholas D., and Bates, Peter W.. "On the singular limit in a phase field model of phase transitions." Annales de l'I.H.P. Analyse non linéaire 5.2 (1988): 141-178. <http://eudml.org/doc/78148>.

@article{Alikakos1988,
author = {Alikakos, Nicholas D., Bates, Peter W.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular perturbation; phase transition; stable solutions},
language = {eng},
number = {2},
pages = {141-178},
publisher = {Gauthier-Villars},
title = {On the singular limit in a phase field model of phase transitions},
url = {http://eudml.org/doc/78148},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Alikakos, Nicholas D.
AU - Bates, Peter W.
TI - On the singular limit in a phase field model of phase transitions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 2
SP - 141
EP - 178
LA - eng
KW - singular perturbation; phase transition; stable solutions
UR - http://eudml.org/doc/78148
ER -

References

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  1. [Am] H. Amann, Dual Semigroups and Second Order Linear Elliptic Boundary Value Problems, Israel J. Math., Vol. 45, 1983, pp. 225-254. Zbl0535.35017MR719122
  2. [AS] N.D. Alikakos and K.C. Shaing, On the Singular Limit for a Class of Problems Modelling Phase Transitions, S.I.A.M. J. Math. Analysis, Vol. 18, No 5, Sept. 1987, pp. 1453-1462. Zbl0649.34055MR902344
  3. [ASi] N.D. Alikakos and H. Simpson, A Variational Approach for a Class of Singular Perturbation Problems and Applications, Proc. Royal Soc. Edinburgh, 107 A, 1987, pp. 27-42. Zbl0651.49011MR918891
  4. [C] G. Caginalp, An Analysis of a Phase Field Model of a Free Boundary, Archive for Rational Mechanics and Analysis, Arch. Rat. Mech. Anal., 92, 1986, pp. 205-245. Zbl0608.35080MR816623
  5. [CF] G. Caginalp and P. Fife, Elliptic Problems Involving Phase Boundaries Satisfying a Curvature Condition, preprint. Zbl0645.35101MR983727
  6. [CM] G. Caginalp and J.B. Mcleod, The Interior Transition Layer for an Ordinary Differential Equation Arising from Solidification Theory, Quarterly of Applied Math (to appear). Zbl0605.34022
  7. [FH] G. Fusco and J. Hale, Stable Equilibria in a Scalar Parabolic Equation with Variable Diffusion, S.I.A.M. J. Math. Anal., Vol. 16, 1985, pp. 1152-1164. Zbl0597.35040MR807902
  8. [MN] J.J. Mahony and J. Norbury, Asymptotic Location of Nodal lines Using Geodesic Theory, J. Australian Math. Soc., Vol. A, January 1986. Zbl0597.35047
  9. [M1] L., Modica, Gradient Theory of Phase Transitions and Minimal Interface Criterion, Arch. Rat. Mech. Anal., 98, 1987, pp. 123-142. Zbl0616.76004MR866718
  10. [M2] L. Modica, Gradient Theory of Phase Transitions with Boundary Contact Energy (to appear). Zbl0642.49009
  11. [MM] L. Modica and S. Mortola, The Γ-Convergence of Some Functionals, Istituto Matematico "Leonida Tonelli", Univ. Pisa Preprint 77-7, 1977. MR473971
  12. [N] I.P. Natanson, Theory of Functions of a Real Vairable, F. Ungar Publishing Co., New York, 1955. Zbl0064.29102MR67952
  13. [S] P. Sternberg, The Effect of a Singular Perturbation on Nonconvex Variational Problems, Ph. D. dissertation, N.Y.U., June 1986. Zbl0647.49021

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