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.

Analysis of a perturbed Cahn–Hilliard model for Langmuir–Blodgett films / Bonacini, Marco; Davoli, Elisa; Morandotti, Marco. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 26:5(2019), pp. 36.1-36.40. [10.1007/s00030-019-0583-5]

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

Bonacini, Marco;
2019

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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Bonacini, Marco; Davoli, Elisa; Morandotti, Marco
Analysis of a perturbed Cahn–Hilliard model for Langmuir–Blodgett films / Bonacini, Marco; Davoli, Elisa; Morandotti, Marco. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 26:5(2019), pp. 36.1-36.40. [10.1007/s00030-019-0583-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/241579
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