CONVERGENCE OF SOLUTIONS TO A CONVECTIVE CAHN-HILLIARD-TYPE EQUATION OF THE SIXTH ORDER IN CASE OF SMALL DEPOSITION RATES
Publication Name
SIAM Journal on Mathematical Analysis
Abstract
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.
Open Access Status
This publication may be available as open access
Volume
55
Issue
5
First Page
5823
Last Page
5861
Funding Number
DP150100375
Funding Sponsor
Australian Research Council