There are a number of important semilinear parabolic partial differential equations, such as the Cahn-Hilliard, the Swift-Hohenberg and the Kuramoto-Sivashinsky equations, which contain a fourth order spatial derivative. Such equations do not, in general, exhibit positivity preservation but may do so under some further restriction on the initial data and parameters; recent results in this area include the study of positivity and convergence of solutions of such equations, by employing generalized energy methods and sharp interpolation inequalities.