MATHEMATICAL SCIENCES COLLOQUIUM

DATE:	November 15th, 2007
TIME:	4:30 - 5:30 PM
PLACE:	LN2205
SPEAKER:	Roberto Triggiani (University of Virginia)
TITLE:	The Parabolic-Hyperbolic PDE System of Fluid-Structure Interaction: Semi-group Well-Posedness, Spectral Analysis, Strong and Exponential Stability, Backward Uniqueness.

Abstract

In 3-d or 2-d, we consider an elastic structure (described by the system of dynamic elasticity, hyperbolic) immersed in a fluid (Navier-Stokes, parabolic), with coupling taking place at the interface; that is, the boundary of the structure. In this preliminary analysis, the elastic structure is fixed but vibrates (small but rapid vibrations). In the case of the linear Navier-Stokes, we shall present the following results:
a) semigroup well posedness in the natural finite enrgy space, with explicit generator;
b) backward uniqueness of such (parabolic-hyperbolic) semigroup;
c) spectral analysis of the generator (and its adjoint);
d) analysis of strong stability of the system;
e) exponential stability of the system, this time with dissipation at the interface.
All these are recent results obtained in several papers jointly with George Avalos (U of Nebraska)

R E F R E S H M E N T S

4:00 to 4:25 PM
Kenneth W. Anderson
Memorial Reading Room