C. Foias's Books

Navier-Stokes Equations and Turbulence

By: C. Foias,O. Manley,R. Rosa,R. Temam

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Navier-Stokes Equations and Turbulence

By: C. Foias,O. Manley,R. Rosa,R. Temam

This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.

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Page Count

363

Publisher

Cambridge University Press

Published Date

ISBN 10

1139428993

ISBN 13

9781139428996

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

By: P. Constantin,C. Foias,B. Nicolaenko,R. Temam

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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

By: P. Constantin,C. Foias,B. Nicolaenko,R. Temam

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.

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Page Count

133

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461235065

ISBN 13

9781461235064

Metric Constrained Interpolation, Commutant Lifting and Systems

By: C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek

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Metric Constrained Interpolation, Commutant Lifting and Systems

By: C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek

This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing.

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Page Count

587

Publisher

Birkhäuser

Published Date

ISBN 10

3034887914

ISBN 13

9783034887915

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

By: Edoardo Mosca,Luciano Pandolfi

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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

By: Edoardo Mosca,Luciano Pandolfi

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

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Page Count

346

Publisher

Springer

Published Date

ISBN 10

3540466045

ISBN 13

9783540466048

Book's by C. Foias

Navier-Stokes Equations and Turbulence

Navier-Stokes Equations and Turbulence

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

Metric Constrained Interpolation, Commutant Lifting and Systems

Metric Constrained Interpolation, Commutant Lifting and Systems

H -Control Theory

H -Control Theory

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