An equation related to the derivative Cahn–Hilliard equation with convection

We consider a nonlinear fourth order evolution equation related to the Convective Cahn–Hilliard equation. We study the asymptotic behaviour of the solutions and find the values of the parameters for which solutions converges to the zero steady state and no patterns are observed in the asymptotic behaviour. In other parameter’s regime we obtain the existence of a global attractor. Moreover we prove the existence of periodic travelling waves. • Convergence to the equilibria. • Existence of a Global Attractor. • Existence of periodic travelling waves.