Analysis and control of dynamic #64258;uid -structure interactions
by
Irena Lasiecka
University of Virginia

Fluid and structure interacting on an interface between the two media is an established model used frequently in engineering and medical applications. The response of the tissue due to radiation force penetrating body fluids or the movement of microbubbles used as dye contrast in ultrasound imaging are just examples of a multitude of applications that motivate studying PDE structure of the underlying model. Fluid-structure intaraction copmprises of Navier Stokes equation and dynamic system of elasticity coupled on the interface between fluid and solid. The coupling is prescribed via matching conditions imposed on Cauchy Polya stress tensors and on velocities. The popularity of the model and its strong link with fundamental applications has generated in recent times a lot of interest in the area. In fact, there are many results pertaining to numerical and experimental treatment of the model. Much less, however, is known with respect to PDE analysis of the system. Questions such as well-posedness of finite energy solutions, or stability and controllability of solutions still present vastly unknown territory. The main aim of this talk is to report some of recent developments in this area, which include topics such as:

Existence and uniqueness of finite energy solutions.

Stability and boundary stabilization of the model.

Optimal control problems and associated Riccati equations with controls acting on the interface.

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Date received: February 24, 2008