Calculus of Variations and Geometric Measure Theory

M. Bonacini - E. Davoli - M. Morandotti

Analysis of a perturbed Cahn-Hilliard model for Langmuir-Blodgett films

created by morandott on 20 Sep 2018
modified on 10 Dec 2019


Published Paper

Inserted: 20 sep 2018
Last Updated: 10 dec 2019

Journal: NoDEA
Year: 2019
Doi: 10.1007/s00030-019-0583-5

ArXiv: 1809.07566 PDF
Links: journal link


An advective Cahn-Hilliard model motivated by thin film formation is studied in this paper. The one-dimensional evolution equation under consideration includes a transport term, whose presence prevents from identifying a gradient flow structure. Existence and uniqueness of solutions, together with continuous dependence on the initial data and an energy equality are proved by combining a minimizing movement scheme with a fixed point argument. Finally, it is shown that, when the contribution of the transport term is small, the equation possesses a global attractor and converges, as the transport term tends to zero, to a purely diffusive Cahn-Hilliard equation.

Keywords: minimizing movements, Thin films, Global attractor, Evolution equations, Cahn-Hilliard equation, Langmuir-Blodgett transfer, fixed point theorem