VERGARA-HERMOSILLA, Gastón; MATIGNON, Denis; TUCSNAK, Marius

doi:10.1016/j.ifacol.2021.06.146

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VERGARA-HERMOSILLA, Gastón
Institut de Mathématiques de Bordeaux [IMB]

MATIGNON, Denis
Département d'Ingénierie des Systèmes Complexes [DISC]

TUCSNAK, Marius
Institut de Mathématiques de Bordeaux [IMB]

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Communication dans un congrès

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IFAC PapersOnline, IFAC PapersOnline, Mathematical Theory of Networks and Systems, 2021-08, Cambridge. 2021, vol. 54, n° 9, p. 205-212

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The PDE system introduced in Maity et al. (2019) describes the interaction of surface water waves with a floating solid, and takes into account the viscosity µ of the fluid. In this work, we study the Cummins type integro-differential equation for unbounded domains, that arises when the system is linearized around equilibrium conditions. A proof of the input-output stability of the system is given, thanks to a diffusive representation of the generalized fractionaloperator $\sqrt{1 + \mu s}$. Moreover, relying on Matignon (1996) stability result for fractional systems,explicit solutions are established both in the frequency and the time domains, leading to an explicit knowledge of the decay rate of the solution. Finally, numerical evidence is provided of the transition between different decay rates as a function of the viscosity $\mu$.< Leer menos

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Fluid-Structure Interaction

Fractional Differential Equations

Asymptotic behaviour

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Asymptotic behaviour of a system modelling rigid structures floating in a viscous fluid

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