James C. Robinson

Infinite-Dimensional Dynamical Systems

An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors
Herausgeber: Crighton, D. G.; Ablowitz, M. J.

• Gebundenes Buch

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 480
• Erscheinungstermin: 26. Mai 2009
• Englisch
• Abmessung: 235mm x 157mm x 33mm
• Gewicht: 924g
• ISBN-13: 9780521632041
• ISBN-10: 0521632048
• Artikelnr.: 21698704

Inhaltsangabe

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.