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September  2008, 3(3): 651-673. doi: 10.3934/nhm.2008.3.651

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

Grigory Panasenko 1, and  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, France
2. 

Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014 700 Bucharest, Romania

Received  April 2008 Published  June 2008

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.
Keywords: elastic membrane, non periodic case, asymptotic expansion, viscous fluid, boundary layer method, Fluid-structure interaction, error estimate.
Mathematics Subject Classification: Primary: 76M45; Secondary: 74F1.
Citation: Grigory Panasenko, Ruxandra Stavre. Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall. Networks & Heterogeneous Media, 2008, 3 (3) : 651-673. doi: 10.3934/nhm.2008.3.651
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