Exact and approximate controllability for distributed parameter systems : a numerical approach / Roland Glowinski, Jacques-Louis Lions, Jiwen He.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Diffusion models -- Distributed and pointwise control for linear diffusion equations -- Boundary control -- Control of the Stokes system -- Control of nonlinear diffusion systems -- Dynamic programming for linear diffusion equations -- Wave models -- Wave equations -- On the application of controllability methods to the solution of the Helmholtz equation at large wave numbers -- Other wave and vibration problems, coupled systems -- Flow control -- Optimal control of systems modelled by the Navier-Stokes equations : application to drag reduction.

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.