In this paper, we propose and study non-overlapping substructuring type algorithms for the Cahn–Hilliard (CH) equation, which was originally proposed to describe phase separation phenomenon binary melted alloy below critical temperature. order develop robust numerical techniques CH present formulation of Dirichlet–Neumann (DN) Neumann–Neumann (NN) methods applied equation their convergence beha...

We analyze the sharp interface limit for Allen–Cahn equation with an anisotropic, spatially periodic mobility coefficient and prove that large-scale behavior of interfaces is determined by mean curvature flow effective mobility. Formally, result follows from asymptotics developed Barles Souganidis bistable reaction–diffusion equations coefficients. However, we show corresponding cell problem ac...

We present efficient, second-order accurate and adaptive finite-difference methods to solve the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface energy anisotropy is sufficiently strong, there are missing orientations in the equilibrium level curves of the diffuse interface solutions, corresponding to those missing from the sharp interface Wulff shape, and...

Abstract A proof of convergence is given for a bulk–surface finite element semidiscretisation the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in smooth domain. The studied an abstract weak formulation as second-order system. Optimal-order uniform-in-time error estimates are shown $L^2$- and $H^1$-norms. based on consistency stability analysis. performed framework,...

multiplicity of positive solutions for a class of semilinear problem. II. Junping Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. multiplicity of positive solutions for a class of semilinear problems. Existence and instability of spike layer solutions to singular perturbation problems. J.