A finite dimensional attractor of the Moore-Greitzer PDE model. (English) Zbl 0926.34040
The Moore-Greitzner PDE model with viscosity is presented and the equations are rewritten as an evolution equation on a Hilbert space. It is proven that the initial value problem 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, invariant set which attracts all bounded sets. Finally, the fractal and Hausdorff dimension of the attractor are estimated.
Reviewer: Norbert Koksch (Dresden)
MSC:
| 34D45 | Attractors of solutions to ordinary differential equations |
| 35K25 | Higher-order parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K55 | Nonlinear parabolic equations |
| 34K23 | Complex (chaotic) behavior of solutions to functional-differential equations |
| 34G20 | Nonlinear differential equations in abstract spaces |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
