Ebook: Infinite-Dimensional Dynamical Systems in Mechanics and Physics

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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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.
Content:
Front Matter....Pages i-xvi
General Introduction. The User’s Guide....Pages 1-14
General Results and Concepts on Invariant Sets and Attractors....Pages 15-40
Elements of Functional Analysis....Pages 41-79
Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations....Pages 80-174
Attractors of Dissipative Wave Equations....Pages 175-248
Lyapunov Exponents and Dimension of Attractors....Pages 249-291
Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems....Pages 292-374
Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions....Pages 375-407
The Cone and Squeezing Properties. Inertial Manifolds....Pages 408-445
Back Matter....Pages 446-501

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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.
Content:
Front Matter....Pages i-xvi
General Introduction. The User’s Guide....Pages 1-14
General Results and Concepts on Invariant Sets and Attractors....Pages 15-40
Elements of Functional Analysis....Pages 41-79
Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations....Pages 80-174
Attractors of Dissipative Wave Equations....Pages 175-248
Lyapunov Exponents and Dimension of Attractors....Pages 249-291
Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems....Pages 292-374
Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions....Pages 375-407
The Cone and Squeezing Properties. Inertial Manifolds....Pages 408-445
Back Matter....Pages 446-501
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