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, M.; Davoli, E.; Morandotti, M.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 26:5(2019).
Titolo: | Analysis of a perturbed Cahn–Hilliard model for Langmuir–Blodgett films |
Autori: | |
Data di pubblicazione: | 2019 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00030-019-0583-5 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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[024]-2019-Bon-Dav-Mor[NoDEA-NDEA-D-19-00122].pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia | |
NDEA-S-19-00146.pdf | 2. Post-print / Author's Accepted Manuscript | Non Pubblico - Accesso privato/ristretto | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2793212