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Autor: Avalos, George (Comienzo)

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Registro 1 de 2, Base de información BIBCYT

Autor:	Avalos, George
Título:	The Strong Stability and Instability of a Fluid-Structure Semigroup
Páginas/Colación:	pp. 163-184

Applied Mathematics & Optimization: An International Journal with Applcations to Stochastics Vol. 55, no. 2 March/April. 2007

Información de existencia

Palabras Claves:

ASYMTOTIC STABILITY,

FLUID-STRUCTURE INTERACTONS,

PARTIAL DIFFERENTIAL EQUATIONS

Resumen
RESUMEN

RESUMEN

The strong stability problem for a fluid-structure interactive partial differential equation (PDE) is considered. The PDE comprises a coupling of the linearized Stokes equations to the classical system of elasticity, with the coupling occurring on the boundary interface between the fluid and solid media. Because of the nature of the unbounded coupling between fluid and structure, the resolvent of the associated semigroup generator will not be a compact operator. In consequence, the classical solution to the stability problem, by means of the Nagy-Foias decomposition, will not avail here. Moreover, it is not practicable to write down explicitly the resolvent of the fluid-structure generator; this situation thus makes it problematic to use the well-known semigroup stability result of Arendt-Batty and Lyubich-Pong. When a locally suported boundary dissipative mechanism is in place, we derive here result of strong decav for this fluid-structure PDE. In the absence of said dissipative mechanism, we show the lack of asymptotic decay for solutions corresponding to arbitrary initial data of finite energy

Registro 2 de 2, Base de información BIBCYT

Referencias Analíticas

Autor:	Avalos, George ; Lasiecka, Irena
Título:	Well-posedness of a Structural Acoustics Control Model with Point Observation of the Pressure
Páginas/Colación:	40-78p
Url:	http://www.idealibrary.com/links/doi/10.1006/jdeq.2000.3938

Journal of Differential Equations Vol. 173, no. 1 June 2001

Información de existencia

Resumen
We consider a controlled and observed partial differential equation (PDE) which describes a structural acoustics interaction. Physically, this PDE describes an acoustic chamber with a flexible chamber wall. The control is applied to this flexible wall, and the class of controls under consideration includes those generated by piezoceramic patches. The observation we consider is point measurements of acoustic pressure inside the cavity. Mathematically, the model consists of a wave equation coupled, through boundary trace terms, to a structurally damped plate (or beam) equation, and the point controls and observations for this system are modeled by highly unbounded operators. We analyze the map from the control to the observation, since the properties of this map are central to any control design which is based upon this observation. We also show there exists an appropriate state space , so that if the initial state is in and the control is in L2, then the state evolves continuously in and the observation is in L2. The analysis of this system entails a microlocal analysis of the wave component of the system, and the use of pseudodifferential machinery

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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