Infinite-dimensional dynamical systems in mechanics and physics /
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations ar...
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| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer,
[1997]
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| Edition: | Second edition. |
| Series: | Applied mathematical sciences (Springer-Verlag New York Inc.) ;
volume 68. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 1. General results and concepts on invariant sets and attractors
- 2. Elements of functional analysis
- 3. Attractors of the dissipative evolution equation of the first order in time: reaction-diffusion equations. Fluid mechanics and pattern formation equations
- 4. Attractors of dissipative wave equations
- 5. Lyapunov exponents and dimensions of attractors
- 6. Explicit bounds on the number of degrees of freedom and the dimension of attractors of some physical systems
- 7. Non-well-posed problems, unstable manifolds, lyapunov functions, and lower bounds on dimensions
- 8. The cone and squeezing properties. Inertial manifolds
- 9. Inertial manifolds and slow manifolds. The non-self-adjoint case
- 10. Approximation of attractors and inertial manifolds. Convergent families of approximate inertial manifolds
- Appendix: Collective Sobolev inequaliies.