March  2008, 9(2): 199-220. doi: 10.3934/dcdsb.2008.9.199

Homogenization and long time asymptotic of a fluid-structure interaction problem

1. 

Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 PALAISEAU Cedex

2. 

Section de Mathématiques, EPFL, 1015 Lausanne, Switzerland

Received  February 2007 Revised  November 2007 Published  December 2007

We study the homogenization of an unsteady fluid-structure interaction problem with a scaling corresponding to a long time asymptotic regime. We consider oscillating initial data which are Bloch wave packets corresponding to tubes vibrating in opposition of phase. We prove that the initial displacements follow the rays of geometric optics and that the envelope function evolves according to a Schr ̈odinger equation which can be interpreted as an effect of dispersion.
Citation: Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199
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