Calculus of Variations and Geometric Measure Theory
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G. Allaire - A. Ferriero

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

created by ferrieroa on 19 Apr 2007
modified on 15 Jun 2010

[BibTeX]

Published Paper

Inserted: 19 apr 2007
Last Updated: 15 jun 2010

Journal: Discrete Contin. Dyn. Syst. Ser. B
Year: 2008

Abstract:

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 Schrödinger equation which can be interpreted as an effect of dispersion.


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