Geodesic
Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method
Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 3-15

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DOI

In this paper, periodic steady-state of a liquid film flowing over a periodic uneven wall is investigated via a classical method. Specifically, we analyze a long-wave model that is valid at the near-critical Reynolds number. For the periodic wall surface, we construct an iteration scheme in terms of an integral form of the original steady-state problem. The uniform convergence of the scheme is proved so that we can derive the existence and the uniqueness as well as the asymptotic formula of the periodic solutions.
DOI : 10.4153/CMB-2017-035-5
Mots-clés : 34E05, 34E10, 34E15, film flow, classical methods, asymptotic analysis 
Alhasanat, Ahmad; Ou, Chunhua. Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method. Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 3-15. doi: 10.4153/CMB-2017-035-5
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     author = {Alhasanat, Ahmad and Ou, Chunhua},
     title = {Periodic {Steady-state} {Solutions} of a {Liquid} {Film} {Model} via a {Classical} {Method}},
     journal = {Canadian mathematical bulletin},
     pages = {3--15},
     year = {2018},
     volume = {61},
     number = {1},
     doi = {10.4153/CMB-2017-035-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-035-5/}
}
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