Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.

Sébastien Court

doi:10.3934/eect.2014.3.83

Article Contents

2014, Volume 3, Issue 1: 83-118. Doi: 10.3934/eect.2014.3.83

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Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.

Sébastien Court^1,

1.
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9

Received: March 2013

Revised: December 2013

Published: March 2014

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Abstract

In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the self-propelled nature of the solid. The proof is based on the boundary feedback stabilization of the linearized system. From this boundary feedback operator we construct a deformation of the solid which satisfies the aforementioned constraints and which stabilizes the nonlinear system. The proof is made by a fixed point method.

Keywords:

Mathematics Subject Classification: Primary: 93C20, 35Q30, 76D05, 76D07, 74F10, 93C05, 93B52, 93D15; Secondary: 74A99, 35Q74.

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