Polynomial decay and control of a 1-d model for fluid-structure interaction.
type: Item
instance of: scholarly article
title: Polynomial decay and control of a 1-d model for fluid-structure interaction.
zbMATH Open document ID: 1083.93024
DOI: 10.1016/S1631-073X(03)00169-9
author: Enrique Zuazua
author: Xu Zhang
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-09-15T00:00:00Z
review text: We consider a linearized and simplified 1-d model for fluid-structure interaction. The domain where the system evolves consists in two bounded intervals in which the wave and heat equations evolve respectively, with transmission conditions at the point of interface. First, we develop a careful spectral asymptotic analysis on high frequencies. Next, according to this spectral analysis we obtain sharp polynomial decay rates for the whole energy of smooth solutions. Finally, we prove the null-controllability of the system when the control acts on the boundary of the interval where the heat equation holds. The proof is based on a new Ingham-type inequality, which follows from the spectral analysis we develop and the null controllability result in E. Zuazua [Menaldi, José Luis (ed.) et al., Optimal control and partial differential equations. In honour of Professor Alain Bensoussan's 60th birthday. Proceedings of the conference, Paris, France, December 4, 2000. Amsterdam: IOS Press; Tokyo: Ohmsha. 198--207 (2001; Zbl 1054.35009)] where the control acts on the wave component.
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74M05
zbMATH DE Number: 1981358
MaRDI profile type: Publication
cites work: Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
cites work: The cost of approximate controllability for heat equations: The linear case
cites work: On exact boundary zero-controllability of two-dimensional Navier-Stokes equations
cites work: Q4040043
cites work: Explicit observability estimate for the wave equation with potential and its application
cites work: Polynomial decay and control of a 1D hyperbolic-parabolic coupled system
cites work: Q3159191
full work available at URL: s1631-073x(03)00169-9
OpenAlex ID: W2082293233
description: scientific article; zbMATH DE number 1981358