@article{AIHPC_1998__15_4_459_0,
author = {Wei, Juncheng and Winter, Matthias},
title = {Stationary solutions for the Cahn-Hilliard equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {15},
year = {1998},
pages = {459-492},
mrnumber = {1632937},
zbl = {0910.35049},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1998__15_4_459_0}
}
Wei, Juncheng; Winter, Matthias. Stationary solutions for the Cahn-Hilliard equation. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) pp. 459-492. http://gdmltest.u-ga.fr/item/AIHPC_1998__15_4_459_0/
[1] , Lectures on Elliptic Boundary Value Problems, Von Nostrand, Princeton, 1965. | MR 178246 | Zbl 0142.37401
[2] , and , Convergence of the Cahn-Hilliard equation to the Hele-Shaw model, Arch. Rat. Mech. Anal., Vol. 128, 1994, pp. 165-205. | MR 1308851 | Zbl 0828.35105
[3] , and , Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eqns., Vol. 90, 1991, pp. 81-134. | MR 1094451 | Zbl 0753.35042
[4] and , The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math., Vol. 53, 1993, pp. 990-1008. | MR 1232163 | Zbl 0788.35061
[5] and , Free energy of a nonuniform system, I. Interfacial free energy, J. Chem. Phys., Vol. 28, 1958, pp. 258-267.
[6] and , Existence of equilibria for the Cahn-Hilliad equation via local minimizers of the perimeter, preprint. | MR 1399196
[7] , A note on asymptotic uniqueness for some nonlinearities which change sign, preprint. | MR 1748710
[8] and , Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, 1986, J. Funct. Anal., Vol. 69, pp. 397-408. | MR 867665 | Zbl 0613.35076
[9] , and , Symmetry of positive solutions of nonlinear elliptic equations in Rn, Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Studies Vol. 7A, pp. 369-402, Academic Press, New York, 1981. | Zbl 0469.35052
[10] and , Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001
[11] and , Counting stationary solutions of the Cahn-Hilliard equation by transversality arguments, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 125, 1995, pp. 351-370. | MR 1331565 | Zbl 0828.34007
[12] and , Multiple wells in the semi-classical limit I, Comm. PDE, Vol. 9, 1984, pp. 337-408. | MR 740094 | Zbl 0546.35053
[13] and , Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 111, 1989, pp. 69-84 | MR 985990 | Zbl 0676.49011
[14] , and , Large amplitude stationary solutions to a chemotaxis systems, J. Diff. Eqns., 1988, Vol. 72, pp. 1-27. | MR 929196 | Zbl 0676.35030
[15] and , Non-Homogeneous Boundary Value Problems and Applications, Vol I, Springer-Verlag, New York/Heidelberg/Berlin, 1972. | MR 350177 | Zbl 0223.35039
[16] , The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., Vol. 107, 1989, pp. 71-83. | MR 1000224 | Zbl 0681.49012
[17] , and , Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J., 1992, Vol. 67, pp. 1-20. | MR 1174600 | Zbl 0785.35041
[18] and , On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 1991, Vol. 41, pp. 819-851. | MR 1115095 | Zbl 0754.35042
[19] and , Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., Vol. 70, 1993, pp. 247-281. | MR 1219814 | Zbl 0796.35056
[20] and , On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math., Vol. 48, 1995, pp. 731-768. | MR 1342381 | Zbl 0838.35009
[21] , Existence of semi-classical bound states of nonlinear Schrödinger equations with potentials of the class (V)a, 1988, Comm. PDE, Vol. 13(12), pp. 1499-1519. | MR 970154 | Zbl 0702.35228
[22] , On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials, 1990, Comm. Math. Phys., Vol. 131, pp. 223-253. | MR 1065671 | Zbl 0753.35097
[23] , Front migration in the nonlinear Cahn-Hilliard equation, Proc. Roy. Soc. London A, Vol. 422, 1989, pp. 261-278. | MR 997638 | Zbl 0701.35159
[24] and , Uniqueness of positive solutions of semilinear equations in Rn, Arch. Rational Mech. Anal., Vol. 81, 1983, pp. 181-197. | MR 682268 | Zbl 0516.35031