Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method. Issue 1 (1st March 2018)

• Record Type: Journal Article
• Authors: Alhasanat, Ahmad; Ou, Chunhua
• Is Part Of: Canadian mathematical bulletin =. Volume 61:Issue 1(2018)
• Page Start: 3
• Page End: 15
• Publication Date: 2018-03-01
• Subjects: 34E05 -- 34E10 -- 34E15; film flow -- classical methods -- asymptotic analysis; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2017-035-5
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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.