Submitted Paper

Inserted: 17 mar 2026
Last Updated: 27 mar 2026

Year: 2026

Abstract:

We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow perturbed by a linear term $\beta u_x$. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small $\beta$ the equation has the structure of gradient flow in a weak sense. Combining this with the finite number of steady states implies stabilization of solutions.

Keywords: Langmuir-Blodgett transfer, stabilization of solutions, gradient-type systems, Cahn-Hilliard type equation

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