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

2013/03/27 by Sébastien Court, Court, Sébastien
Mathematics · #35Q30 #35Q74 #74F10 #76D05 #76D07 #93B52 #93C05 #93D15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Primary: 93C20 #Secondary: 74A99 #math.AP #math.OC #msc:35Q30 #msc:35Q74 #msc:74A99 #msc:74F10 #msc:76D05 #msc:76D07 #msc:93B52 #msc:93C05 #msc:93C20 #msc:93D15

paper · pdf · doi:10.48550/arxiv.1303.6834

37 pages, 1 figure

arxiv created 2014/01/02 · arxiv updated 2014/01/06

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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