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arXiv · 1303.6834

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

Sébastien Court
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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.

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Sébastien Court. 2014-01-02. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system. https://arxiv.org/abs/1303.6834

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