Return to Colloquia & Seminar listing
Center Manifold of a Nonlinear Partial Differential Equation that models Compressor Systems
Student-Run Research Seminar| Speaker: | MingQing Xiao, Mathematics, UC Davis |
| Location: | 593 Kerr |
| Start time: | Wed, Apr 28 1999, 4:10PM |
A commonly used mathematical model that captures the flow behavior of a compression system, due to Moore and Greitzer, consists of a PDE and two ODEs. The PDE describes the behavior of disturbances in the inlet region of compression system, and the two ODEs describe the coupling of the disturbances with the mean flow.
In this talk I will first introduce this model, and then show that the PDE system features a local center manifold. The significance of this result is that a study of the behavior of the local flow in the compressor can thus be translated into a study of the flow of two scalar differential equations on the center manifold. The result is obtained by converting the original PDE system into an evolution equation on a Hilbert space, and showing that this equation and its linearized version (around a desired equilibrium) are not topologically equivalent. I will further discuss the stability of the flow, using the reduced two dimensional system.
The talk will conclude with a discussion of some control issues that arise in the stabilization of the flow through compressor systems, and some underlying mathematical challenges.