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Periodic steady-state solutions of a liquid film model via a classical method

  • Ahmad Alhasanat,
    Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada, A1C 5S7
  • Chunhua Ou,
    Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada, A1C 5S7
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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.
Keywords: film flow, classical methods, asymptotic analysis film flow, classical methods, asymptotic analysis
MSC Classifications: 34E05, 34E10, 34E15 show english descriptions Asymptotic expansions
Perturbations, asymptotics
Singular perturbations, general theory
34E05 - Asymptotic expansions
34E10 - Perturbations, asymptotics
34E15 - Singular perturbations, general theory
 

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