Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model

Barbu, Viorel; Grujić, Zoran; Lasiecka, Irena; Tuffaha, Amjad

doi:10.1090/conm/440/08476

Cited by 78 publications

(148 citation statements)

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“…In Sect. 2.1 we shall recall, for the reader's convenience, the theory in [8] that is needed for our purposes.…”

Section: The Pde Model Statement Of Main Resultsmentioning

confidence: 99%

“…Further technical results obtained in [8] and [26] will be needed in the proof of our main result; these will be recorded in an Appendix for convenience.…”

Section: Variational and Semigroup Formulationmentioning

confidence: 99%

“…Section 4 contains the proof of Theorem 2.6, based upon the application of the theory in [2]. Finally, a short Appendix collects the statements of the regularity results pertaining to the elastic component of the system-recently obtained in [8] and [26]-which are crucially utilized in the proof of Theorem 2.10.…”

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confidence: 99%

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Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Bucci

Lasiecka

2009

Calc. Var.

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We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the fluid component of the system, which are then applied to show well-posedness of the Differential Riccati Equations arising in the optimization problem. This yields the feedback synthesis of the unique optimal control, under a very weak constraint on the observation operator; in particular, the present analysis allows general functionals, such as the integral of the natural energy of the physical system. Furthermore, this work confirms that the theory developed in Acquistapace et al. (Adv Diff Eq,[2])-crucially utilized here-encompasses widely differing PDE problems, from thermoelastic systems to models of acoustic-structure and, now, fluid-structure interactions.

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“…In Sect. 2.1 we shall recall, for the reader's convenience, the theory in [8] that is needed for our purposes.…”

Section: The Pde Model Statement Of Main Resultsmentioning

confidence: 99%

“…Further technical results obtained in [8] and [26] will be needed in the proof of our main result; these will be recorded in an Appendix for convenience.…”

Section: Variational and Semigroup Formulationmentioning

confidence: 99%

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Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Bucci

Lasiecka

2009

Calc. Var.

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“…FSI problems coupling the Navier-Stokes equations with linear elasticity where the coupling was calculated at a fixed fluid domain boundary, were considered in [23], and in [2,3,35] where an additional nonlinear coupling term was added at the interface. A study of well-posedness for FSI problems between an incompressible, viscous fluid and an elastic/viscoelastic structure with nonlinear coupling evaluated at a moving interface started with the result by daVeiga [4], where existence of a strong solution was obtained locally in time for an interaction between a 2D fluid and a 1D viscoelastic string, assuming periodic boundary conditions.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof

Muha

Čanić

2013

Communications in Information and Systems

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We study a 3D fluid-structure interaction (FSI) problem between an incompressible, viscous fluid modeled by the Navier-Stokes equations, and the motion of an elastic structure, modeled by the linearly elastic cylindrical Koiter shell equations, allowing structure displacements that are not necessarily radially symmetric. The problem is set on a cylindrical domain in 3D, and is driven by the time-dependent inlet and outlet dynamic pressure data. The coupling between the fluid and the structure is fully nonlinear (2-way coupling), giving rise to a nonlinear, moving-boundary problem in 3D. We prove the existence of a weak solution to this 3D FSI problem by using an operator splitting approach in combination with the Arbitrary Lagrangian Eulerian mapping, which satisfies a geometric conservation law property. We effectively prove that the resulting computational scheme converges to a weak solution of the full, nonlinear 3D FSI problem.

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“…Backward uniqueness results for the present parabolic-hyperbolic model (1.5) with η = 0 and its simplified canonical model are given in [10,11], respectively. The nonlinear fluid case (Navier-Stokes) is studied in [14,15] by a variational approach. A companion result for a hyperbolic/parabolic system arising in structural acoustics is given in [4].…”

Section: Preliminary Dissipation Identitymentioning

confidence: 99%

Boundary feedback stabilization of a coupled parabolic–hyperbolic Stokes–Lamé PDE system

Avalos

Triggiani

2009

J. Evol. Equ.

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We consider a parabolic-hyperbolic coupled system of two partial differential equations (PDEs), which governs fluid-structure interactions, and which features a suitable boundary dissipation term at the interface between the two media. The coupled system consists of Stokes flow coupled to the Lamé system of dynamic elasticity, with the respective dynamics being coupled on a boundary interface, where dissipation is introduced. Such a system is semigroup well-posed on the natural finite energy space (Avalos and Triggiani in Discr Contin Dynam Sys, to appear). Here we prove that, moreover, such semigroup is uniformly (exponentially) stable in the corresponding operator norm, with no geometrical conditions imposed on the boundary interface. This result complements the strong stability properties of the undamped case (Avalos and Triggiani in Discr Contin Dynam Sys, to appear).

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Existence of the energy-level weak solutions for a nonlinear fluid-structure interaction model

Cited by 78 publications

References 0 publications

Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

Optimal boundary control with critical penalization for a PDE model of fluid–solid interactions

A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof

Boundary feedback stabilization of a coupled parabolic–hyperbolic Stokes–Lamé PDE system

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