On the singular limit in a phase field model of phase transitions
Alikakos, Nicholas D. ; Bates, Peter W.
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988), p. 141-178 / Harvested from Numdam
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@article{AIHPC_1988__5_2_141_0,
     author = {Alikakos, Nicholas D. and Bates, Peter W.},
     title = {On the singular limit in a phase field model of phase transitions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {5},
     year = {1988},
     pages = {141-178},
     mrnumber = {954469},
     zbl = {0696.35060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1988__5_2_141_0}
}

Alikakos, Nicholas D.; Bates, Peter W. On the singular limit in a phase field model of phase transitions. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) pp. 141-178. http://gdmltest.u-ga.fr/item/AIHPC_1988__5_2_141_0/

[Am] H. Amann, Dual Semigroups and Second Order Linear Elliptic Boundary Value Problems, Israel J. Math., Vol. 45, 1983, pp. 225-254. | MR 719122 | Zbl 0535.35017

[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. | MR 902344 | Zbl 0649.34055

[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. | MR 918891 | Zbl 0651.49011

[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. | MR 816623 | Zbl 0608.35080

[CF] G. Caginalp and P. Fife, Elliptic Problems Involving Phase Boundaries Satisfying a Curvature Condition, preprint. | MR 983727 | Zbl 0645.35101

[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). | MR 840451 | Zbl 0605.34022

[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. | MR 807902 | Zbl 0597.35040

[MN] J.J. Mahony and J. Norbury, Asymptotic Location of Nodal lines Using Geodesic Theory, J. Australian Math. Soc., Vol. A, January 1986. | MR 814402 | Zbl 0597.35047

[M1] L., Modica, Gradient Theory of Phase Transitions and Minimal Interface Criterion, Arch. Rat. Mech. Anal., 98, 1987, pp. 123-142. | MR 866718 | Zbl 0616.76004

[M2] L. Modica, Gradient Theory of Phase Transitions with Boundary Contact Energy (to appear). | Numdam | Zbl 0642.49009

[MM] L. Modica and S. Mortola, The Γ-Convergence of Some Functionals, Istituto Matematico "Leonida Tonelli", Univ. Pisa Preprint 77-7, 1977. | MR 473971

[N] I.P. Natanson, Theory of Functions of a Real Vairable, F. Ungar Publishing Co., New York, 1955. | MR 67952 | Zbl 0064.29102

[S] P. Sternberg, The Effect of a Singular Perturbation on Nonconvex Variational Problems, Ph. D. dissertation, N.Y.U., June 1986.