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,...

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...

We study the asymptotic behavior of classical solutions to an initial-boundary value problem (IBVP) for a coupled Cahn-Hilliard-Boussinesq system on bounded domains with large initial data. A sufficient condition is established under which the solutions decay exponentially to constant states as time approaches infinity.

The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model describing Langmuir-Blodgett transfer is studied. The occurring locking effects enable a control mechanism for the pattern formation process. In the one-dimensional case the parameter range in which patterns are created is increased and the patterns' properties can be adjusted in a broader ...

Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench, periodic stripe patterns are generated behind the quench front. Their wavelength is uniquely defined by the velocity of the quench interface in a wide range. Numerical simulations match perfectly analytical results obta...