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

ISBN-13: 9780521885720 / Angielski / Twarda / 2008 / 470 str.

Jacques-Louis Lions; Jiwen He; R. Glowinski

Opis

This book investigates how a user or observer can influence the behavior of 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 the first part of the book, the authors discuss the mathematics and numerics relating to the controllability of systems modeled by linear and non-linear diffusion equations; Part two is dedicated to the controllability of vibrating systems, typical ones being those modeled by linear wave equations; and finally, part three covers flow control for systems governed by the Navier-Stokes equations modeling 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.

Recenzje

"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

Spis treści

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.