Stabilization of solutions to a model of Langmuir-Blodgett films
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 β ux. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small β 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.
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