On the Cahn–Hilliard Equation with Degenerate Mobility
- 1 March 1996
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 27 (2), 404-423
- https://doi.org/10.1137/s0036141094267662
Abstract
An existence result for the Cahn–Hilliard equation with a concentration dependent diffusional mobility is presented. In particular, the mobility is allowed to vanish when the scaled concentration takes the values $ pm 1$, and it is shown that the solution is bounded by 1 in magnitude. Finally, applications of our method to other degenerate fourth-order parabolic equations are discussed.
Keywords
This publication has 18 references indexed in Scilit:
- The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvatureEuropean Journal of Applied Mathematics, 1996
- The viscous Cahn-Hilliard equation. I. ComputationsNonlinearity, 1995
- Overview no. 113 surface motion by surface diffusionActa Metallurgica et Materialia, 1994
- The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysisEuropean Journal of Applied Mathematics, 1992
- Source type solutions of a fourth order nonlinear degenerate parabolic equationNonlinear Analysis, 1992
- The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysisEuropean Journal of Applied Mathematics, 1991
- Higher order nonlinear degenerate parabolic equationsJournal of Differential Equations, 1990
- Lineare FunktionalanalysisPublished by Springer Science and Business Media LLC ,1985
- Spinodal decomposition: A repriseActa Metallurgica, 1971
- Free Energy of a Nonuniform System. I. Interfacial Free EnergyThe Journal of Chemical Physics, 1958