CONVERGENCE OF SOLUTIONS TO A CONVECTIVE CAHN-HILLIARD-TYPE EQUATION OF THE SIXTH ORDER IN CASE OF SMALL DEPOSITION RATES

We show stabilization of solutions to the sixth-order convective Cahn-Hilliard equation. The problem has the structure of a gradient flow perturbed by a quadratic destabilizing term with coefficient delta > 0. Through application of an abstract result by Carvalho, Langa, and Robinson we show that for small delta the equation has the structure of gradient flow in a weak sense. On the way we prove a kind of Liouville theorem for eternal solutions to parabolic problems. Finally, the desired stabilization follows from a powerful theorem due to Hale and Raugel.

Automated summary

This paper shows the stabilization of solutions to the sixth-order convective Cahn-Hilliard equation. By applying an abstract result by Carvalho, Langa, and Robinson, it is proved that for small delta, the equation has the structure of gradient flow in a weak sense. The desired stabilization is obtained through a powerful theorem due to Hale and Raugel. The importance of this article lies in providing a significant approach to solve the problem by citing other research and applying theorems.