A Finite Dimensional Attractor of the Moore-Greitzer PDE Model

A Finite Dimensional Attractor of the Moore-Greitzer PDE Model

The Moore-Greitzer PDE model with viscosity is presented and the equations are rewritten as an evolution equation on a Hilbert space. It is proven that the model has a unique global solution which is smooth in space and time. Furthermore it is proven that there exists a global attractor, i.e., a com...

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Veröffentlicht in:SIAM Journal of Applied Mathematics 1998-11, Vol.59 (2), p.636-650
Hauptverfasser: Birnir, Bjorn, Hauksson, Hoskuldur Ari
Format: Artikel
Sprache:eng
Schlagworte:
A priori knowledge
ADVANCED PROPULSION SYSTEMS
Air compressors
Applied mathematics
Approximation
ATTRACTORS
Boundary conditions
Cubic polynomials
Engines
Evolution equations
Fractal dimensions
FRACTALS
GAS TURBINE ENGINES
Grants
Hausdorff dimensions
HILBERT SPACE
Jet engines
MATHEMATICAL MODELS
Mathematics
MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS
PARTIAL DIFFERENTIAL EQUATIONS
Stall
Viscosity
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Zusammenfassung:The Moore-Greitzer PDE model with viscosity is presented and the equations are rewritten as an evolution equation on a Hilbert space. It is proven that the model has a unique global solution which is smooth in space and time. Furthermore it is proven that there exists a global attractor, i.e., a compact set which attracts all bounded sets. Finally it is shown that the attractor has a finite fractal dimension.
ISSN:0036-1399
1095-712X
DOI:10.1137/S0036139997325527