Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.

Navier-Stokes Equations (Chicago Lectures in Mathematics)

Science & Math

Constantin, Peter

Foias, Ciprian

Mathematics

Univ of Chicago Pr

Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.

Reference

Almanacs & Yearbooks

University of Chicago Press

The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold--that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.

The Connection Between Infinite Dimensional and Finite Dimensional Dynamical Systems: Proceedings of the Ams-Ims-Siam Joint Summer Research Conferen (Contemporary Mathematics)

Society for Industrial and Applied Mathematics

Institute of Mathematical Statistics

Ams-Ims-Siam Joint Summer Research Conference in the Mathematical Scie

American Mathematical Society

Nicolaenko, Basil

Amer Mathematical Society

The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

Harmonic Analysis of Operators on Hilbert Space (Universitext)

Bercovici, Hari

Kérchy, László

Sz. Nagy, Bela

Springer

Since its inception in the early 1980s, H( optimization theory has become the control methodology of choice in robust feedback analysis and design. The purpose of this monograph is to present, in a tutorial fashion, a self contained operator theoretic approach to the H( control for disturbed parameter systems, that is, systems which admit infinite dimensional state spaces. Such systems arise for problems modelled by partial differential equations or which have time delays. Besides elucidating the mathematics of H( control, extensive treatment is given to its physical and engineering underpinnings. The techniques given in the book are carefully illustrated by two benchmark problems: an unstable system with a time delay which comes from the control of the X-29, and the control of a Euler-Bernoulli flexible beam with Kelvin-Voigt damping.

Robust Control of Infinite Dimensional Systems: Frequency Domain Methods (Lecture Notes in Control and Information Sciences, 209)

Computers & Technology

Computer Science

The fundamental problem in control engineering is to provide robust performance to uncertain plants. H -control theory began in the early eighties as an attempt to lay down rigorous foundations on the classical robust control requirements. It now turns out that H -control theory is at the crossroads of several important directions of research space or polynomial approach to control and classical interpolation theory; harmonic analysis and operator theory; minimax LQ stochastic control and integral equations. The book presents the underlying fundamental ideas, problems and advances through the pen of leading contributors to the field, for graduate students and researchers in both engineering and mathematics. From the Contents: C. Foias: Commutant Lifting Techniques for Computing Optimal H Controllers.- B.A. Francis: Lectures on H Control and Sampled-Data Systems.- J.W. Helton: Two Topics in Systems Engineering Frequency Domain Design and Nonlinear System.- H. Kwakernaak: The Polynomial Approach to H -Optimal Regulation.- J.B. Pearson: A Short Course in l - Optimal Control

H -Control Theory: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Como, Italy, June 18-26, 1990 (Lecture Notes in Mathematics, 1496)

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