Exact and Approximate Controllability for Distributed Parameter Systems

Exact and Approximate Controllability for Distributed Parameter Systems : A Numerical Approach

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The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically, these methods being validated by the results of numerical experiments. In Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of use to more advanced practitioners.
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Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 51 b/w illus. 10 colour illus. 20 tables
  • 1139239392
  • 9781139239394

Table of contents

Preface; Introduction; Part I. Diffusion Models: 1. Distributed and point-wise control for linear diffusion equations; 2. Boundary control; 3. Control of the Stokes system; 4. Control of nonlinear diffusion systems; 5. Dynamic programming for linear diffusion equations; Part II. Wave Models: 6. Wave equations; 7. Helmholtz equation; 8. Coupled systems; Part III. Flow Control: 9. Optimal control of Navier-Stokes equations: drag reduction; Epilogue; Further acknowledgements; References.
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Review quote

"The book definitely has the perfume of those that Lions wrote during his prolific career. My congratulations to his two coworkers for having completed this task that reminded incomplete when he passed away in 2001. This book definitely fills a gap in the existing in literature on control and numerics of PDS, and I am sure it will influence future research in this area."
Enrique Zuazua, Mathematical Reviews
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About Jacques-Louis Lions

Roland Glowinski is Cullen Professor of Mathematics at the University of Houston and Emeritus Professor at Laboratoire J. L. Lions, University P. and M. Curie, Paris. He is a Member of the French National Academy of Sciences and in 2004 won the Von Karman prize from the Society for Industrial and Applied Mathematics. He has written over 300 research papers and this is his 3rd book. The late Jacques-Louis Lions was a Professor at College de France, Paris. During his distinguished career he was elected an honorary member of over twenty learned societies and academies world-wide and received honorary degrees from nineteen universities. He was awarded a large number of international prizes, including the SIAM T and Idalia Reid Prize in Mathematics, the Prize of Japan and the John Von Neumann Prize. By the time of his death in 2001, he had authored over 20 books. Jiwen He is Associate Professor of Mathematics at the University of Houston. His research interests are numerical analysis, computational fluid dynamics, and control theory.
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