New Travelling Wave Solutions of Conformable Cahn-Hilliard Equation

Stationary Solutions for the Cahn-hilliard Equation

We study the Cahn-Hilliard equation in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has a nongenerate critical point. Then we show that there exists a spike-like stationary solution whose global maximum lies on the boundary. Our method is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem. Résumé. Nous étudions l’équat...

The Cahn-hilliard Equation

1. Steady states. There are many two component systems in which phase separation can be induced by rapidly cooling the system. Thus, if a two component system, which is spatially uniform at temperature T1, is rapidly cooled to a second sufficiently lower temperature T2, then the cooled system will separate into regions of higher and lower concentration. A phenomenological description of the beh...

The Cahn–Hilliard Equation

Spectral Analysis of Stationary Solutions of the Cahn–Hilliard Equation

For the Cahn–Hilliard equation on R, there are precisely three types of bounded non-constant stationary solutions: periodic solutions, pulse-type reversal solutions, and monotonic transition waves. We study the spectrum of the linear operator obtained upon linearization about each of these waves, establishing linear stability for all transition waves, linear instability for all reversal waves, ...

Interface Solutions of a Degenerate Cahn - Hilliard Equation

We present an analysis of the equilibrium diiusive interfaces in a model for the interaction of layers of pure polymers. The discussion focuses on the important qualitative features of the solutions of the nonlinear singular Cahn-Hilliard equation with degenerate mobility for the Flory-Huggins-de Gennes free energy model. The spatial structure of possible equilibrium phase separated solutions a...