Exact and Approximate Controllability for Distributed Parameter Systems

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.

• Computationally oriented with a thorough discussion of the solution methods employed in the various chapters (finite element methods, conjugate gradient algorithms and more)
• Blends mathematical analysis and numerical analysis and illustrates with a large variety of numerical experiments
• One of the few books on controllability issues for systems modelled by partial differential equations from mechanics and physics, a hot topic at the moment