Periodic stationary patterns governed by a convective Cahn-Hilliard equation

We investigate bifurcations of stationary periodic solutions of a convective Cahn-Hilliard equation, u(t)+Duu(x)+(u-u(3)+u(xx))(xx) = 0, describing phase separation in driven systems, and study the stability of the main family of these solutions. For the driving parameter D < D-0 = root 2/ 3, the periodic stationary solutions are unstable. For D > D-0, the periodic stationary solutions are stable if their wavelength belongs to a certain stability interval. It is therefore shown that in a driven phase-separating system that undergoes spinodal decomposition the coarsening can be stopped by the driving force, and formation of stable periodic structures is possible. The modes that destroy the stability at the boundaries of the stability interval are also found.