James C. RobinsonInfinite-Dimensional Dynamical Systems
An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors
Herausgeber: Ablowitz, M. J.; Crighton, D. G.
Part I. Functional Analysis: 1. Banach and Hilbert spaces
2. Ordinary differential equations
3. Linear operators
4. Dual spaces
5. Sobolev spaces
Part II. Existence and Uniqueness Theory: 6. The Laplacian
7. Weak solutions of linear parabolic equations
8. Nonlinear reaction-diffusion equations
9. The Navier-Stokes equations existence and uniqueness
Part II. Finite-Dimensional Global Attractors: 10. The global attractor existence and general properties
11. The global attractor for reaction-diffusion equations
12. The global attractor for the Navier-Stokes equations
13. Finite-dimensional attractors: theory and examples
Part III. Finite-Dimensional Dynamics: 14. Finite-dimensional dynamics I, the squeezing property: determining modes
15. Finite-dimensional dynamics II, The stong squeezing property: inertial manifolds
16. Finite-dimensional dynamics III, a direct approach
17. The Kuramoto-Sivashinsky equation
Appendix A. Sobolev spaces of periodic functions
Appendix B. Bounding the fractal dimension using the decay of volume elements.
