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Periodic Steady-state Solutions of a Liquid Film Model via a Classical Method

Published online by Cambridge University Press:  20 November 2018

Ahmad Alhasanat  and
Chunhua Ou
Ahmad Alhasanat
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S6, e-mail: [email protected] [email protected]
Chunhua Ou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S6, e-mail: [email protected] [email protected]
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Abstract

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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.

Keywords

34E0534E1034E15film flowclassical methodsasymptotic analysis
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 3 - 15
Copyright
Copyright © Canadian Mathematical Society 2018

References

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