Infinite-Dimensional Dynamical Systems in Mechanics and Physics
By: by Roger Temam
Series: Applied Mathematical Sciences -- 68; Applied mathematical sciences (Springer-Verlag New York Inc.) -- 68.
Publisher: Springer US
Published: 1988
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 500
ISBN-13: 9781468403152; 9781468403138
Subjects: Mathematics; Global analysis (Mathematics)
Description: This book is the first attempt for a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics, along with other areas of science and technology. A synthetic view of the relation between infinite and finite dimensional systems is presented. Equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau and damped wave. The last chapter of the book introduces inertial manifolds, a subject of rapid development.
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Table of contents: title: General Introduction. The User's Guide. General Results and Concepts on Invariant Sets and Attractors; title: Elements of Functional Analysis; title: Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction-Diffusion Equations. Fluid Mechanics and Pattern Formation Equations; title: Attractors of Dissipative Wave Equations; title: Lyapunov Exponents and Dimension of Attractors; title: Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems; title: Non- Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions; title: The Cone and Squeezing Properties. Inertial Monifolds; title: Appendix: Collective Sobolev Inequalities; title: Bibliography; title: Index.