This is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.
Contents: General Introduction. The User's Guide. General Results and Concepts on Invariant Sets and Attractors.- Elements of Functional Analysis.- Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction-Diffusion Equations. Fluid Mechanics and Pattern Formation Equations.- Attractors of Dissipative Wave Equations.- Lyapunov Exponents and Dimension of Attractors.- Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems.- Non- Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions.- The Cone and Squeezing Properties. Inertial Monifolds.- Appendix: Collective Sobolev Inequalities.- Bibliography.- Index.
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Softcover reprint of the original 1st ed. 1988