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Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 651-673. doi: 10.3934/nhm.2008.3.651
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Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall

  • 1.
    Laboratory of Mathematics of the University of Saint-Etienne (LaMUSE), University Jean Monnet, 23, rue Dr Paul Michelon 42023 Saint-Etienne
  • 2.
    Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014 700 Bucharest
  • Received: 01 April 2008

  • Primary: 76M45; Secondary: 74F10.

  • In this paper we continue the study of a fluid-structure interaction problem with the non periodic case. We consider the non stationary flow of a viscous fluid in a thin rectangle with an elastic membrane as the upper part of the boundary. The physical problem which corresponds to non homogeneous boundary conditions is stated. By using a boundary layer method, an asymptotic solution is proposed. The properties of the boundary layer functions are established and an error estimate is obtained.

    Citation: Grigory Panasenko, Ruxandra Stavre. Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall[J]. Networks and Heterogeneous Media, 2008, 3(3): 651-673. doi: 10.3934/nhm.2008.3.651

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  • In this paper we continue the study of a fluid-structure interaction problem with the non periodic case. We consider the non stationary flow of a viscous fluid in a thin rectangle with an elastic membrane as the upper part of the boundary. The physical problem which corresponds to non homogeneous boundary conditions is stated. By using a boundary layer method, an asymptotic solution is proposed. The properties of the boundary layer functions are established and an error estimate is obtained.


  • This article has been cited by:

    1. Grigory Panasenko, Ruxandra Stavre, Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel, 2010, 5, 1556-181X, 783, 10.3934/nhm.2010.5.783
    2. Ruxandra Stavre, A boundary control problem for the blood flow in venous insufficiency. The general case, 2016, 29, 14681218, 98, 10.1016/j.nonrwa.2015.11.003
    3. G. P. Panasenko, R. Stavre, Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow, 2014, 24, 0218-2025, 1781, 10.1142/S0218202514500079
    4. Grigory Panasenko, Konstantin Pileckas, Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. I. The case without boundary-layer-in-time, 2015, 122, 0362546X, 125, 10.1016/j.na.2015.03.008
    5. Irina Malakhova-Ziablova, Grigory Panasenko, Ruxandra Stavre, Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem, 2016, 95, 0003-6811, 1467, 10.1080/00036811.2015.1132311
    6. Grigory P. Panasenko, Ruxandra Stavre, 2010, Chapter 13, 978-1-4419-1342-5, 275, 10.1007/978-1-4419-1343-2_13
    7. R. Fares, G. P. Panasenko, R. Stavre, A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis, 2012, 2012, 1085-3375, 1, 10.1155/2012/152743
    8. G.P. Panasenko, R. Stavre, Asymptotic analysis of the Stokes flow in a thin cylindrical elastic tube, 2012, 91, 0003-6811, 1999, 10.1080/00036811.2011.584187
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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