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arXiv · 1809.07566

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

Marco Bonacini·Elisa Davoli·Marco Morandotti
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Abstract

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.

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Marco Bonacini, Elisa Davoli, Marco Morandotti. 2018-09-20. Analysis of a perturbed Cahn-Hilliard model for Langmuir-Blodgett films. https://arxiv.org/abs/1809.07566

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