# Mathematics Colloquia and Seminars

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### Center Manifold of a Nonlinear PDE That Models Compressor Systems

**Mathematical Physics & Probability**

Speaker: | Dr. MingQing Xiao, UC Davis |

Location: | 693 kerr |

Start time: | Tue, Jun 8 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 it will be shown 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. The stability of the flow will be discussed through 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.