@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}, mrnumber = {1632937}, zbl = {0910.35049}, language = {en}, url = {http://www.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 SP - 459 EP - 492 VL - 15 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org./item/AIHPC_1998__15_4_459_0/ LA - en ID - AIHPC_1998__15_4_459_0 ER -
Wei, Juncheng; Winter, Matthias. Stationary solutions for the Cahn-Hilliard equation. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 4, pp. 459-492. http://www.numdam.org./item/AIHPC_1998__15_4_459_0/
[1] Lectures on Elliptic Boundary Value Problems, Von Nostrand, Princeton, 1965. | MR | Zbl
,[2] Convergence of the Cahn-Hilliard equation to the Hele-Shaw model, Arch. Rat. Mech. Anal., Vol. 128, 1994, pp. 165-205. | MR | Zbl
, and ,[3] Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eqns., Vol. 90, 1991, pp. 81-134. | MR | Zbl
, and ,[4] The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math., Vol. 53, 1993, pp. 990-1008. | MR | Zbl
and ,[5] Free energy of a nonuniform system, I. Interfacial free energy, J. Chem. Phys., Vol. 28, 1958, pp. 258-267.
and ,[6] Existence of equilibria for the Cahn-Hilliad equation via local minimizers of the perimeter, preprint. | MR
and ,[7] A note on asymptotic uniqueness for some nonlinearities which change sign, preprint. | MR
,[8] Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, 1986, J. Funct. Anal., Vol. 69, pp. 397-408. | MR | Zbl
and ,[9] 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
, and ,[10] Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin, 1983. | MR | Zbl
and ,[11] 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
and ,[12] Multiple wells in the semi-classical limit I, Comm. PDE, Vol. 9, 1984, pp. 337-408. | MR | Zbl
and ,[13] Local minimizers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A, Vol. 111, 1989, pp. 69-84 | MR | Zbl
and ,[14] Large amplitude stationary solutions to a chemotaxis systems, J. Diff. Eqns., 1988, Vol. 72, pp. 1-27. | MR | Zbl
, and ,[15] Non-Homogeneous Boundary Value Problems and Applications, Vol I, Springer-Verlag, New York/Heidelberg/Berlin, 1972. | MR | Zbl
and ,[16] The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal., Vol. 107, 1989, pp. 71-83. | MR | Zbl
,[17] 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
, and ,[18] On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 1991, Vol. 41, pp. 819-851. | MR | Zbl
and ,[19] Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., Vol. 70, 1993, pp. 247-281. | MR | Zbl
and ,[20] 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
and ,[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 | Zbl
,[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 | Zbl
,[23] Front migration in the nonlinear Cahn-Hilliard equation, Proc. Roy. Soc. London A, Vol. 422, 1989, pp. 261-278. | MR | Zbl
,[24] Uniqueness of positive solutions of semilinear equations in Rn, Arch. Rational Mech. Anal., Vol. 81, 1983, pp. 181-197. | MR | Zbl
and ,