Abstract: In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a boundary interface with a two-dimensional mechanical plate equation. In the case that the PDE plate component is rotational inertia-free, one will have that solutions of this fluid-structure PDE system exhibit an exponential rate of decay. By way of proving this decay, an estimate is obtained for the resolvent of the associated semigroup generator, an estimate which is uniform for frequency domain values along the imaginary axis. Subsequently, we proceed to discuss relevant point control and boundary control scenarios for this fluid-structure PDE model, with an ultimate view to optimal control studies on both finite and infinite horizon. (Because of said exponential stability result, optimal control of the PDE on time interval (0, ∞) becomes a reasonable problem for contemplation.)

Exponential decay properties of a mathematical model for a certain fluid-structure interaction / Avalos, George; Bucci, Francesca. - STAMPA. - (2014), pp. 49-78. [10.1007/978-3-319-11406-4_3]

Exponential decay properties of a mathematical model for a certain fluid-structure interaction

BUCCI, FRANCESCA
2014

Abstract

Abstract: In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a boundary interface with a two-dimensional mechanical plate equation. In the case that the PDE plate component is rotational inertia-free, one will have that solutions of this fluid-structure PDE system exhibit an exponential rate of decay. By way of proving this decay, an estimate is obtained for the resolvent of the associated semigroup generator, an estimate which is uniform for frequency domain values along the imaginary axis. Subsequently, we proceed to discuss relevant point control and boundary control scenarios for this fluid-structure PDE model, with an ultimate view to optimal control studies on both finite and infinite horizon. (Because of said exponential stability result, optimal control of the PDE on time interval (0, ∞) becomes a reasonable problem for contemplation.)
2014
9783319114064
New Prospects in Direct, Inverse and Control Problems for Evolution Equations
49
78
Goal 17: Partnerships for the goals
Avalos, George; Bucci, Francesca
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/859494
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