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Local controllability for a “swimming” model. (English) Zbl 1137.76077

Summary: We study the local controllability of a mathematical model of an abstract object which “swims” in two-dimensional nonstationary Stokes fluid. We assume that this object consists of finitely many subsequently connected small sets (“thick points”), each of which can act upon any of the adjacent sets in a rotation fashion with the purpose of generating its fish- or snake-like motion. We regard the magnitudes of the respective rotation forces, entering the system’s equations as coefficients, as multiplicative (or bilinear) controls. The structural integrity of the object is maintained by elastic forces acting between the aforementioned adjacent sets according to Hooke’s law. Models like this are of a interest in biology and engineering applications dealing with propulsion systems in fluids.

MSC:

76Z10 Biopropulsion in water and in air
76D55 Flow control and optimization for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
92C10 Biomechanics
93C20 Control/observation systems governed by partial differential equations
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