The Open Applied Mathematics Journal

2013, 7 : 1-17
Published online 2013 September 03. DOI: 10.2174/1874114220130430001
Publisher ID: TOAMJ-7-1

Min-max Game Theory for Elastic and Visco-Elastic Fluid Structure Interactions

Irena Lasiecka , Roberto Triggiani and Jing Zhang
Department of Mathematics, University of Virginia, Charlottesville, VA 22901, USA.

ABSTRACT

We present the salient features of a min-max game theory developed in the context of coupled PDE's with an interface. Canonical applications include linear fluid-structure interaction problem modeled by Oseen's equations coupled with elastic waves. We shall consider two models for the structures: elastic and visco-elastic. Control and disturbance are allowed to act at the interface between the two media. The sought-after saddle solutions are expressed in a pointwise feedback form, which involves a Riccati operator; that is, an operator satisfying a suitable non-standard Riccati differential equation. Motivations, applications as well as a brief historical account are also provided.

Keywords:

Elasticity, fluid-structure interactions, min-max game problem, Riccati operator, visco-elasticity.