Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall

Grigory Panasenko; Ruxandra Stavre; Grigory Panasenko; Ruxandra Stavre

doi:10.3934/nhm.2008.3.651

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

Grigory Panasenko ^{1
,},
Ruxandra Stavre ^{2
,}

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.
- Fluid-structure interaction,
- viscous fluid,
- elastic membrane,
- asymptotic expansion,
- non periodic case,
- boundary layer method,
- error estimate
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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Abstract

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.
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