Consider the so-called higher-order convective Cahn-Hilliard equation
together with the standard Cahn-Hilliard equation
The stationary solutions obtained by solving the resulting, by letting , ordinary differential equation together with their stability are considered. They are discussed with the far-field conditions as boundary value conditions
with some integration constant. The whole paper is concerned only with stationary solutions in one dimension hence with various asymptotics with respect to and .