http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Infinite-dimensional dynamical systems in mechanics and physics
1 online resource (xxi, 648 pages) : illustrations.
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 arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
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.
Includes bibliographical references (pages [613]-643) and index.
Applied mathematical sciences (Springer-Verlag New York Inc.) ; volume 68