Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

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.