Sensitivity analysis for a free boundary fluid-elasticity interaction

Lorena Bociu; Jean-Paul Zolésio

doi:10.3934/eect.2013.2.55

Article Contents

2013, Volume 2, Issue 1: 55-79. Doi: 10.3934/eect.2013.2.55

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Sensitivity analysis for a free boundary fluid-elasticity interaction

Lorena Bociu^1, and
Jean-Paul Zolésio^2,

1.
NC State University, Department of Mathematics, 3236 SAS Hall, Raleigh, NC 27695-8205
2.
CNRS-INLN, 1361 Routes des Lucioles, Sophia Antipolis, F-06560 Valbonne

Received: May 31, 2012

Revised: August 31, 2012

Published: February 2013

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Abstract

In this paper a total linearization is derived for the free boundary nonlinear elasticity - incompressible fluid interaction. The equations and the free boundary are linearized together and the new linearization turns out to be different from the usual coupling of classical linear models. New extra terms are present on the common interface, some of them involving the boundary curvatures. These terms play an important role in the final linearized system and can not be neglected.

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Mathematics Subject Classification: Primary: 93B35, 93B18, 74F10, 35R35; Secondary: 74B20, 35Q30.

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