Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

被引:3
|
作者
Mitra, Debanjana [1 ]
Roy, Arnab [2 ]
Takahashi, Takeo [3 ]
机构
[1] Indian Inst Technol, Dept Math, Powai 400076, Maharashtra, India
[2] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567 1, Czech Republic
[3] Univ Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
关键词
Fluid-structure interaction systems; Viscoelastic fluids; Controllability; Stabilizability; Finite-dimensional controls; LOCAL NULL CONTROLLABILITY; BOUNDARY CONTROLLABILITY; SHEAR-FLOW; MAXWELL;
D O I
10.1007/s00498-021-00295-x
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We study control properties of a linearized fluid-structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that as in the case without structure, the system is not exactly null-controllable in finite time.
引用
收藏
页码:637 / 667
页数:31
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