The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase
separation in binary alloys by Cahn and Hilliard. Since then the equation has been …

We present an explicit conservative Saul'yev finite difference scheme for the Cahn–Hilliard
(CH) equation, which models a phase separation phenomenon in binary alloys. The CH …

We consider an optimal control problem of tracking type governed by a time-discrete
regularized phase-field fracture or damage propagation model. The energy minimization …

Abstract The space fractional Cahn–Hilliard phase-field model is more adequate and
accurate in the description of the formation and phase change mechanism than the classical …

The present contribution investigates shape optimization problems for a class of semilinear
elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and …

In this paper, we consider the radial basis function collocation method with fictitious centres
for solving the Cahn–Hilliard equation in one-dimensional and two-dimensional settings …

This paper proposes a benchmark problem for the two-and three-dimensional Cahn–Hilliard
(CH) equations, which describe the process of phase separation. The CH equation is highly …

We prove second-order optimality conditions for an optimal control problem of tracking-type
for a time-discrete regularized phase-field fracture or damage propagation model. The …

We prove local quadratic convergence of the sequential quadratic programming (SQP)
method for an optimal control problem of tracking type governed by one time step of the …

This chapter focuses on a doubly nonlocal Cahn–Hilliard system that involves weakly
singular kernels in the operators and which allows discontinuous solutions. The system is …