Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation (Mathématiques et Applications Book 66)

From the reviews: “This book is an introduction to the mathematical control theory of some applied partial differential equations. ... The material in this book is a nice simplification of that from the existing advanced monographs on infinite-dimensional control theory. ... This text can be used as a textbook for a one-semester graduate course on control theory for the systems governed by partial differential equations.” (Xu Zhang, Mathematical Reviews, Issue 2010 m) “This book is an introductory text in control theory of partial differential equations (PDEs) intended for first-year graduate students in mathematics or engineering ... . book is well thought out and the topics flow together nicely. ... This textbook would be very suitable as a primary text for a course on control theory of PDEs that emphasizes application of feedback stabilization theory to concrete PDEs. ... also serve as a valuable side reference in a more general or abstract course with its many excellent examples.” (Scott W. Hansen, SIAM Review, Vol. 53 (2), 2011) "This book addresses the feedback stabilization of the linear reaction-convection-diffusion equation and the linear wave equation. Both interior and boundary control problems are discussed. Methods employed to handle the problems include the eigenfunction expansion, integral transform, perturbed energy method, and optimal control technique. These powerful methods are frequently used for solving control problems of partial differential equations. Unlike the existing advanced control theory books written in an abstract setting, this book presents control theory by means of concrete examples. Therefore, this book is easy to read. Once readers learn about the ideas and methods from these concrete control examples, they can apply them to solve other control problems of partial differential equations."--Publisher's website Front Matter....Pages I-X Examples of Control Systems....Pages 1-7 Elementary Functional Analysis....Pages 9-48 Finite Dimensional Systems....Pages 49-117 Linear Reaction-Convection-Diffusion Equation....Pages 119-214 One-dimensional Wave Equation....Pages 215-231 Higher-dimensional Wave Equation....Pages 233-292 Back Matter....Pages 293-296 Unlike abstract approaches to advanced control theory, this volume presents key concepts through concrete examples. Once the basic fundamentals are established, readers can apply them to solve other control problems of partial differential equations.