Stationary solutions for the Cahn-Hilliard equation
Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 4, pp. 459-492.
@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},
pages = {459--492},
publisher = {Gauthier-Villars},
volume = {15},
number = {4},
year = {1998},
zbl = {0910.35049},
mrnumber = {1632937},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1998__15_4_459_0/}
}
TY  - JOUR
AU  - Wei, Juncheng
AU  - Winter, Matthias
TI  - Stationary solutions for the Cahn-Hilliard equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1998
DA  - 1998///
SP  - 459
EP  - 492
VL  - 15
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1998__15_4_459_0/
UR  - https://zbmath.org/?q=an%3A0910.35049
UR  - https://www.ams.org/mathscinet-getitem?mr=1632937
LA  - en
ID  - AIHPC_1998__15_4_459_0
ER  - 
%0 Journal Article
%A Wei, Juncheng
%A Winter, Matthias
%T Stationary solutions for the Cahn-Hilliard equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 1998
%P 459-492
%V 15
%N 4
%I Gauthier-Villars
%G en
%F 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, Volume 15 (1998) no. 4, pp. 459-492. http://archive.numdam.org/item/AIHPC_1998__15_4_459_0/

[1] S. Agmon, Lectures on Elliptic Boundary Value Problems, Von Nostrand, Princeton, 1965. | MR | Zbl

[2] N. Alikakos, P.W. Bates and X. Chen, Convergence of the Cahn-Hilliard equation to the Hele-Shaw model, Arch. Rat. Mech. Anal., Vol. 128, 1994, pp. 165-205. | MR | Zbl

[3] N. Alikakos, P.W. Bates and G. Fusco, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eqns., Vol. 90, 1991, pp. 81-134. | MR | Zbl

[4] P.W. Bates and P.C. Fife, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math., Vol. 53, 1993, pp. 990-1008. | MR | Zbl

[5] J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system, I. Interfacial free energy, J. Chem. Phys., Vol. 28, 1958, pp. 258-267.

[6] X. Chen and M. Kowalczyk, Existence of equilibria for the Cahn-Hilliad equation via local minimizers of the perimeter, preprint. | MR

[7] E.N. Dancer, A note on asymptotic uniqueness for some nonlinearities which change sign, preprint. | MR

[8] A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, 1986, J. Funct. Anal., Vol. 69, pp. 397-408. | MR | Zbl

[9] B. Gidas, W.-M. Ni and L. Nirenberg, 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

[10] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin, 1983. | MR | Zbl

[11] M. Grinfeld and A. Novick-Cohen, Counting stationary solutions of the Cahn-Hilliard equation by transversality arguments, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 125, 1995, pp. 351-370. | MR | Zbl

[12] B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I, Comm. PDE, Vol. 9, 1984, pp. 337-408. | MR | Zbl

[13] R.V. Kohn and P. Sternberg, Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 111, 1989, pp. 69-84 | MR | Zbl

[14] C.-S. Lin, W.-M. Ni and I. Takagi, Large amplitude stationary solutions to a chemotaxis systems, J. Diff. Eqns., 1988, Vol. 72, pp. 1-27. | MR | Zbl

[15] J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol I, Springer-Verlag, New York/Heidelberg/Berlin, 1972. | MR | Zbl

[16] L. Modica, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., Vol. 107, 1989, pp. 71-83. | MR | Zbl

[17] W.-M. Ni, X. Pan and I. Takagi, 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 | Zbl

[18] W.-M. Ni and I. Takagi, On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 1991, Vol. 41, pp. 819-851. | MR | Zbl

[19] W.-M. Ni and I. Takagi, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., Vol. 70, 1993, pp. 247-281. | MR | Zbl

[20] W.-M. Ni and J. Wei, 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 | Zbl

[21] Y.G. Oh, 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 | Zbl

[22] Y.G. Oh, On positive multi-lump bound states of nonlinear Schrödinger equations under multiple-well potentials, 1990, Comm. Math. Phys., Vol. 131, pp. 223-253. | MR | Zbl

[23] R.L. Pego, Front migration in the nonlinear Cahn-Hilliard equation, Proc. Roy. Soc. London A, Vol. 422, 1989, pp. 261-278. | MR | Zbl

[24] L.A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in Rn, Arch. Rational Mech. Anal., Vol. 81, 1983, pp. 181-197. | MR | Zbl