Counting stationary solutions of the Cahn–Hilliard equation by transversality arguments

[1]  J. Chadam,et al.  Nonlinear Partial Differential Equations and Applications , 1978 .

[2]  Peter W. Bates,et al.  The Dynamics of Nucleation for the Cahn-Hilliard Equation , 1993, SIAM J. Appl. Math..

[3]  P. Sternberg The effect of a singular perturbation on nonconvex variational problems , 1988 .

[4]  Konstantin Mischaikow,et al.  Global asymptotic dynamics of gradient-like bistable equations , 1995 .

[5]  L. Modica The gradient theory of phase transitions and the minimal interface criterion , 1987 .

[6]  M. Mimura,et al.  Stationary states associated with phase separation in a pure material. I. The large latent heat case , 1989 .

[7]  M. Gurtin,et al.  Structured phase transitions on a finite interval , 1984 .

[8]  L. Peletier,et al.  Steady states of the one-dimensional Cahn–Hilliard equation , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[9]  Morton E. Gurtin,et al.  On the structure of equilibrium phase transitions within the gradient theory of fluids , 1988 .

[10]  Zheng Songmu,et al.  Asymptotic behavior of solution to the Cahn-Hillard equation , 1986 .

[11]  Amy Novick-Cohen,et al.  On Cahn-Hilliard type equations , 1990 .

[12]  Peter W. Bates,et al.  Slow motion for the Cahn-Hilliard equation in one space dimension , 1991 .

[13]  J. Carr,et al.  Metastable patterns in solutions of ut = ϵ2uxx − f(u) , 1989 .

[14]  L. Segel,et al.  Nonlinear aspects of the Cahn-Hilliard equation , 1984 .

[15]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[16]  P. Freitas,et al.  A nonlocal Sturm–Liouville eigenvalue problem , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  J. Furter,et al.  On a stationary state characterization of transition from spinodal decomposition to nucleation behaviour in the Cahn-Hilliard model of phase separation , 1989 .

[18]  Charles M. Elliott,et al.  On the Cahn-Hilliard equation , 1986 .

[19]  Joel Smoller,et al.  Global Bifurcation of Steady-State Solutions , 1981 .

[20]  J. Furter,et al.  A monotonicity theorem and its application to stationary solutions of the phase field model , 1992 .

[21]  J. Rubinstein,et al.  Nonlocal reaction−diffusion equations and nucleation , 1992 .

[22]  James D. Gunton,et al.  Introduction to the Theory of Metastable and Unstable States , 1983 .

[23]  Danielle Hilhorst,et al.  On the slow dynamics for the Cahn–Hilliard equation in one space dimension , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[24]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

[25]  Stephan Luckhaus,et al.  The Gibbs-Thompson relation within the gradient theory of phase transitions , 1989 .

[26]  Jack K. Hale,et al.  Slow-motion manifolds, dormant instability, and singular perturbations , 1989 .

[27]  Roger Temam,et al.  Some Global Dynamical Properties of a Class of Pattern Formation Equations , 1989 .

[28]  Jan A. Sanders,et al.  A codimension two bifurcation with a third order Picard-Fuchs equation , 1985 .