Control Problems for Strongly Coupled Non-Linear Partial Differential Equations

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

The present research project aims at investigating the properties of control, optimization, stability and long-time behavior of interactive structures, which are mathematically modeled by inhomogeneous systems of strongly coupled partial differential equations with an interface. Both the single partial differential equations describing each a constitutive component of the overall structure as well as the coupling between them, may be linear or non-linear, dispersive, and oscillatory. <br><br> Investigation will be carried out initially on four canonical motivating classes of interactive structures. They are intended to serve as benchmark cases for the general topic of physically significant interactive and non-trivially coupled Partial Differential Equations. They are: (1) the noise reduction problem in a structural acoustic chamber, by use of 'smart material/structure' technology; (2) flutter control of a 2-dimensional wing immersed in a subsonic or supersonic 3-dimensional gas flow in aeroelasticity; (3) plasma heating and plasma confinement in the control of magnetohydrodynamics equations; (4) asymptotic suppression of turbulence in viscous incompressible fluid dynamics.