The Iitaka conjecture predicts that if $f\colon X\to Y$ is a fibration of smooth complex projective varieties and $y\in Y$ is a general point, then $\kappa(K_X)\geq \kappa(K_{X_y})+\kappa(K_Y)$. It was shown by Chang that, if the stable base locus $\mathbf{B}(-K_X)$ does not dominate $Y$, then $\kappa(-K_X)\leq \kappa (K_{X_y})+\kappa(-K_Y)$. Both the Iitaka conjecture and Chang's theorem are false in characteristic $p>0$. However the expectation is that one should be able to recover these inequalities when a general fiber is sufficiently "well behaved" with respect to the action of Frobenius. In this talk I will discuss how to recover Chang's theorem for such a class of fibrations, and discuss some related questions. This is based on a joint work with M. Benozzo and C.K. Chang.