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

摘要

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