CONVERGENCE OF SOLUTIONS TO A CONVECTIVE CAHN-HILLIARD-TYPE EQUATION OF THE SIXTH ORDER IN CASE OF SMALL DEPOSITION RATES
SIAM Journal on Mathematical Analysis
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.
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Australian Research Council